Pub Date : 2023-12-19DOI: 10.1007/s40687-023-00413-y
Pablo Blanco, Matija Bucić
The Erdős-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general n-vertex graph, if one imposes even a little bit of structure on the graph, namely by forbidding a fixed graph H as an induced subgraph, instead of only being able to find a polylogarithmic size clique or an independent set, one can find one of polynomial size. Despite being the focus of considerable attention over the years, the conjecture remains open. In this paper, we improve the best known lower bound of (2^{Omega (sqrt{log n})}) on this question, due to Erdős and Hajnal from 1989, in the smallest open case, namely when one forbids a (P_5), the path on 5 vertices. Namely, we show that any (P_5)-free n-vertex graph contains a clique or an independent set of size at least (2^{Omega (log n)^{2/3}}). We obtain the same improvement for an infinite family of graphs.
{"title":"Towards the Erdős-Hajnal conjecture for $$P_5$$ -free graphs","authors":"Pablo Blanco, Matija Bucić","doi":"10.1007/s40687-023-00413-y","DOIUrl":"https://doi.org/10.1007/s40687-023-00413-y","url":null,"abstract":"<p>The Erdős-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general <i>n</i>-vertex graph, if one imposes even a little bit of structure on the graph, namely by forbidding a fixed graph <i>H</i> as an induced subgraph, instead of only being able to find a polylogarithmic size clique or an independent set, one can find one of polynomial size. Despite being the focus of considerable attention over the years, the conjecture remains open. In this paper, we improve the best known lower bound of <span>(2^{Omega (sqrt{log n})})</span> on this question, due to Erdős and Hajnal from 1989, in the smallest open case, namely when one forbids a <span>(P_5)</span>, the path on 5 vertices. Namely, we show that any <span>(P_5)</span>-free <i>n</i>-vertex graph contains a clique or an independent set of size at least <span>(2^{Omega (log n)^{2/3}})</span>. We obtain the same improvement for an infinite family of graphs.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"23 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-15DOI: 10.1007/s40687-023-00412-z
Bernhard Heim, Markus Neuhauser
The zeros of the nth D’Arcais polynomial, also known in combinatorics as the Nekrasov–Okounkov polynomial, dictate the vanishing properties of the nth Fourier coefficients of all complex powers x of the Dedekind (eta )-function. In this paper, we prove that these coefficients are non-vanishing for (vert x vert > kappa , (n-1)) and (kappa approx 9.7225). Numerical computations imply that 9.72245 is a lower bound for (kappa ). This significantly improves previous results by Kostant, Han, and Heim–Neuhauser. The polynomials studied in this paper include Chebyshev polynomials of the second kind, 1-associated Laguerre polynomials, Hermite polynomials, and polynomials associated with overpartitions and plane partitions.
第n个D 'Arcais多项式(在组合学中也称为Nekrasov-Okounkov多项式)的零点决定了Dedekind (eta ) -函数的所有复幂x的第n个傅立叶系数的消失性质。在本文中，我们证明了这些系数对于(vert x vert > kappa , (n-1))和(kappa approx 9.7225)是不消失的。数值计算表明，9.72245是(kappa )的下界。这大大改进了Kostant、Han和Heim-Neuhauser先前的结果。本文研究的多项式包括第二类Chebyshev多项式、1相关的Laguerre多项式、Hermite多项式、过分割多项式和平面分割多项式。
{"title":"Estimate for the largest zeros of the D’Arcais polynomials","authors":"Bernhard Heim, Markus Neuhauser","doi":"10.1007/s40687-023-00412-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00412-z","url":null,"abstract":"<p>The zeros of the <i>n</i>th D’Arcais polynomial, also known in combinatorics as the Nekrasov–Okounkov polynomial, dictate the vanishing properties of the <i>n</i>th Fourier coefficients of all complex powers <i>x</i> of the Dedekind <span>(eta )</span>-function. In this paper, we prove that these coefficients are non-vanishing for <span>(vert x vert > kappa , (n-1))</span> and <span>(kappa approx 9.7225)</span>. Numerical computations imply that 9.72245 is a lower bound for <span>(kappa )</span>. This significantly improves previous results by Kostant, Han, and Heim–Neuhauser. The polynomials studied in this paper include Chebyshev polynomials of the second kind, 1-associated Laguerre polynomials, Hermite polynomials, and polynomials associated with overpartitions and plane partitions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"51 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-12DOI: 10.1007/s40687-023-00414-x
Philip A. Etter, Lexing Ying
{"title":"Operator shifting for noisy elliptic systems","authors":"Philip A. Etter, Lexing Ying","doi":"10.1007/s40687-023-00414-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00414-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"82 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1007/s40687-023-00411-0
Daniel Alpay, Ilwoo Cho
Abstract The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a $$C^{*}$$ C∗ -subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of $$left( 2times 2right) $$ 2×2 -block operator matrices.
摘要本文的主要目的是:(i)将尺度超复结构推广到算子值情况，其中算子值取自可分Hilbert空间上算子代数的$$C^{*}$$ C * -子代数;(ii)刻画了(i)的算子值尺度超复结构的可逆性条件;(iii)研究了(ii)的尺度超复数的可逆性与(ii)的算子值情况的可逆性之间的关系。并且(iv)证实了(ii)和(iii)的可逆性等价于$$left( 2times 2right) $$ 2 × 2块算子矩阵的一般可逆性。
{"title":"Certain invertible operator-block matrices induced by $$C^{*}$$-algebras and scaled hypercomplex numbers","authors":"Daniel Alpay, Ilwoo Cho","doi":"10.1007/s40687-023-00411-0","DOIUrl":"https://doi.org/10.1007/s40687-023-00411-0","url":null,"abstract":"Abstract The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a $$C^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> -subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of $$left( 2times 2right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> -block operator matrices.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"44 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The tension determination problem for an inextensible interface in 2D Stokes flow","authors":"Po-Chun Kuo, Ming-Chih Lai, Yoichiro Mori, Analise Rodenberg","doi":"10.1007/s40687-023-00406-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00406-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1007/s40687-023-00409-8
Pu-Zhao Kow, Jenn-Nan Wang
{"title":"Inverse problems for some fractional equations with general nonlinearity","authors":"Pu-Zhao Kow, Jenn-Nan Wang","doi":"10.1007/s40687-023-00409-8","DOIUrl":"https://doi.org/10.1007/s40687-023-00409-8","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1007/s40687-023-00408-9
Andrei Jaikin-Zapirain
Abstract Let $${mathcal {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> be the pseudovariety $${mathcal {F}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> of all finite groups or the pseudovariety $${mathcal {S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> of all finite solvable groups and let $$Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> be either a finitely generated free group or a surface group. The $${mathcal {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> -genus of $$Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> , denoted by $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , consists of the isomorphism classes of finitely generated residually- $$mathcal C$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> groups G having the same quotients in $${mathcal {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> as $$Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> . We show that the groups from $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are residually- p for all primes p . This answers a question of Gilbert Baumslag and shows that the groups in the genus are residually finite rationally solvable groups. This leads to a positive solution of particular case of a question of Alexander Grothendieck: if F is a free group, G is a finitely generated residually- $${mathcal {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> group and $$u:Frightarrow G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>:</mml:mo> <mml:mi>F</mml:mi> <mml:mo>→</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> is a homomorphism such that the induced map of pro- $${mathcal {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> completions $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mover> <mml:mi>C</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:msub> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mover> <mml:mi>C</
抽象Let $${mathcal {C}}$$ C是伪变种 $${mathcal {F}}$$ 所有有限群的F或伪簇 $${mathcal {S}}$$ 所有有限可解群的S，让 $$Gamma $$ Γ要么是有限生成的自由群，要么是曲面群。The $${mathcal {C}}$$ 的C属 $$Gamma $$ Γ，用表示 $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ gc (Γ)，由有限生成残差的同构类组成 $$mathcal C$$ C组G有相同的商 $${mathcal {C}}$$ 选C。 $$Gamma $$ Γ。我们展示了来自 $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ G C (Γ)对所有素数p都是残差p。这回答了Gilbert Baumslag的一个问题，并证明了属中的群是剩余有限合理可解群。这就得到了Alexander Grothendieck问题的一个特殊情况的正解:如果F是一个自由群，则G是一个有限生成的残差 $${mathcal {C}}$$ C组和 $$u:Frightarrow G$$ u: F→G是一个同态，使得pro-的诱导映射 $${mathcal {C}}$$ C完井 $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ u C ^: F C ^→G C ^是同构的，那么u也是同构的。
{"title":"The finite and solvable genus of finitely generated free and surface groups","authors":"Andrei Jaikin-Zapirain","doi":"10.1007/s40687-023-00408-9","DOIUrl":"https://doi.org/10.1007/s40687-023-00408-9","url":null,"abstract":"Abstract Let $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> be the pseudovariety $${mathcal {F}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> of all finite groups or the pseudovariety $${mathcal {S}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> of all finite solvable groups and let $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> be either a finitely generated free group or a surface group. The $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> -genus of $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> , denoted by $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , consists of the isomorphism classes of finitely generated residually- $$mathcal C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> groups G having the same quotients in $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> as $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> . We show that the groups from $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are residually- p for all primes p . This answers a question of Gilbert Baumslag and shows that the groups in the genus are residually finite rationally solvable groups. This leads to a positive solution of particular case of a question of Alexander Grothendieck: if F is a free group, G is a finitely generated residually- $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> group and $$u:Frightarrow G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>:</mml:mo> <mml:mi>F</mml:mi> <mml:mo>→</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> is a homomorphism such that the induced map of pro- $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> completions $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mover> <mml:mi>C</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:msub> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mover> <mml:mi>C</","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"439 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-04DOI: 10.1007/s40687-023-00407-w
Wuchen Li, Siting Liu, Stanley Osher
{"title":"A kernel formula for regularized Wasserstein proximal operators","authors":"Wuchen Li, Siting Liu, Stanley Osher","doi":"10.1007/s40687-023-00407-w","DOIUrl":"https://doi.org/10.1007/s40687-023-00407-w","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"190 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1007/s40687-023-00405-y
Fabian Reede
Abstract Let X be a K3 surface. We prove that Addington’s $$mathbb {P}^n$$ Pn -functor between the derived categories of X and the Hilbert scheme of points $$X^{[k]}$$ X[k] maps stable vector bundles on X to stable vector bundles on $$X^{[k]}$$ X[k] , given some numerical conditions are satisfied.
设X是一个K3曲面。在一定的数值条件下，证明了Addington的$$mathbb {P}^n$$ P n -函子在X的衍生范畴和点$$X^{[k]}$$ X [k]的Hilbert格式之间将X上的稳定向量束映射到$$X^{[k]}$$ X [k]上的稳定向量束。
{"title":"Stability and certain $$mathbb {P}^n$$-functors","authors":"Fabian Reede","doi":"10.1007/s40687-023-00405-y","DOIUrl":"https://doi.org/10.1007/s40687-023-00405-y","url":null,"abstract":"Abstract Let X be a K3 surface. We prove that Addington’s $$mathbb {P}^n$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> -functor between the derived categories of X and the Hilbert scheme of points $$X^{[k]}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:msup> </mml:math> maps stable vector bundles on X to stable vector bundles on $$X^{[k]}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:msup> </mml:math> , given some numerical conditions are satisfied.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1007/s40687-023-00402-1
Cristina Ballantine, Hannah E. Burson, William Craig, Amanda Folsom, Boya Wen
{"title":"Hook length biases and general linear partition inequalities","authors":"Cristina Ballantine, Hannah E. Burson, William Craig, Amanda Folsom, Boya Wen","doi":"10.1007/s40687-023-00402-1","DOIUrl":"https://doi.org/10.1007/s40687-023-00402-1","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号