Pub Date : 2023-12-26DOI: 10.1080/10586458.2023.2293285
Khalil Ayadi, Takao Komatsu
In this article, we show that Zaremba’s conjecture holds for positive integers that appear as values of polynomials resulting from a recurrence formula and their powers of two. For example, Zaremba...
{"title":"Continued Fraction Expansions Towards Zaremba’s Conjecture","authors":"Khalil Ayadi, Takao Komatsu","doi":"10.1080/10586458.2023.2293285","DOIUrl":"https://doi.org/10.1080/10586458.2023.2293285","url":null,"abstract":"In this article, we show that Zaremba’s conjecture holds for positive integers that appear as values of polynomials resulting from a recurrence formula and their powers of two. For example, Zaremba...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-21DOI: 10.1080/10586458.2023.2294827
Tobias Boege
A rational probability distribution on four binary random variables X,Y,Z,U is constructed which satisfies the conditional independence relations [X⊥⊥Y],[X⊥⊥Z|U],[Y⊥⊥U|Z] and [Z⊥⊥U|XY] but whose ...
{"title":"No Eleventh Conditional Ingleton Inequality","authors":"Tobias Boege","doi":"10.1080/10586458.2023.2294827","DOIUrl":"https://doi.org/10.1080/10586458.2023.2294827","url":null,"abstract":"A rational probability distribution on four binary random variables X,Y,Z,U is constructed which satisfies the conditional independence relations [X⊥⊥Y],[X⊥⊥Z|U],[Y⊥⊥U|Z] and [Z⊥⊥U|XY] but whose ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"69 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-21DOI: 10.1080/10586458.2023.2293283
Ján Mináč, Tung T. Nguyen, Nguyễn Duy Tân
For each prime number p one can associate a Fekete polynomial with coefficients–1 or 1 except the constant term, which is 0. These are classical polynomials that have been studied extensively in th...
对于每个质数 p，我们都可以联想到一个系数为 1 或 1 的 Fekete 多项式，但常数项除外，因为常数项为 0。 这些都是经典的多项式，在数学界已被广泛研究。
{"title":"On the Arithmetic of Generalized Fekete Polynomials","authors":"Ján Mináč, Tung T. Nguyen, Nguyễn Duy Tân","doi":"10.1080/10586458.2023.2293283","DOIUrl":"https://doi.org/10.1080/10586458.2023.2293283","url":null,"abstract":"For each prime number p one can associate a Fekete polynomial with coefficients–1 or 1 except the constant term, which is 0. These are classical polynomials that have been studied extensively in th...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"310 5 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-19DOI: 10.1080/10586458.2023.2293292
Rimma Hämäläinen, Jason Lo, Edward Morales
On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifyi...
{"title":"Intersection Numbers on Fibrations and Catalan Numbers","authors":"Rimma Hämäläinen, Jason Lo, Edward Morales","doi":"10.1080/10586458.2023.2293292","DOIUrl":"https://doi.org/10.1080/10586458.2023.2293292","url":null,"abstract":"On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifyi...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"49 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-19DOI: 10.1080/10586458.2023.2294184
Angsuman Das
In this paper, we introduce and study the iterates of the following family of functions φk defined on natural numbers which exhibits nice properties.φk(x)={x+k, if x is prime;largest prime divisor ...
φk(x)={x+k，如果 x 是素数；最大素除数...
{"title":"A Family of Iterated Maps on Natural Numbers","authors":"Angsuman Das","doi":"10.1080/10586458.2023.2294184","DOIUrl":"https://doi.org/10.1080/10586458.2023.2294184","url":null,"abstract":"In this paper, we introduce and study the iterates of the following family of functions φk defined on natural numbers which exhibits nice properties.φk(x)={x+k, if x is prime;largest prime divisor ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138819323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-02DOI: 10.1080/10586458.2021.1980753
Chris Anderson, Kenneth L. Baker, Xinghua Gao, Marc Kegel, Khanh Le, Kyle Miller, Sinem Onaran, Geoffrey Sangston, Samuel Tripp, Adam Wood, Ana Wright
ABSTRACT In Dunfield’s catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in S, we determine that 22 have tunnel number 2 while the remaining all have tunnel number 1. Notably, these 22 manifolds contain 9 asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these 22 knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus 12 and braid index 4.
摘要 在邓菲尔德（Dunfield）的 SnapPy 普查双曲流形目录（SnapPy 普查中的双曲流形是 S 中 L 空间结的补集）中，我们确定有 22 个流形的隧道编号为 2，而其余所有流形的隧道编号均为 1。值得注意的是，这 22 个流形包含 9 个非对称 L 空间结补集。此外，利用 SnapPy 和 KLO，我们还找到了这 22 个结的正辫状闭包，实现了辫状指数的莫顿-弗兰克斯-威廉姆斯约束。其中最小的绳结属数为 12，辫状指数为 4。
{"title":"L-space knots with tunnel number >1 by experiment","authors":"Chris Anderson, Kenneth L. Baker, Xinghua Gao, Marc Kegel, Khanh Le, Kyle Miller, Sinem Onaran, Geoffrey Sangston, Samuel Tripp, Adam Wood, Ana Wright","doi":"10.1080/10586458.2021.1980753","DOIUrl":"https://doi.org/10.1080/10586458.2021.1980753","url":null,"abstract":"ABSTRACT In Dunfield’s catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in S, we determine that 22 have tunnel number 2 while the remaining all have tunnel number 1. Notably, these 22 manifolds contain 9 asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these 22 knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus 12 and braid index 4.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"52 1","pages":"600 - 614"},"PeriodicalIF":0.5,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139324653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-03DOI: 10.1080/10586458.2023.2239265
E. Fuchs, M. Litman, J. Silverman, Austin Tran
{"title":"Orbits on K3 Surfaces of Markoff Type","authors":"E. Fuchs, M. Litman, J. Silverman, Austin Tran","doi":"10.1080/10586458.2023.2239265","DOIUrl":"https://doi.org/10.1080/10586458.2023.2239265","url":null,"abstract":"","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45496980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-21DOI: 10.1080/10586458.2023.2219071
W. Duke
. Certain higher Rademacher symbols are defined that give class functions on the modular group. Their basic properties are derived via a two-variable reformulation of Eichler-Shimura cohomology. This reformulation better explains the role of cycle integrals and leads to new evaluations. The Rademacher symbols determine the values at non-positive integers of the zeta function for a narrow ideal class of a real quadratic field. This result is equivalent to one of Siegel, but is proven in a new way by using an identity for the value of such a zeta function at a positive integer greater than one as a sum of certain double zeta values defined for the quadratic field.
{"title":"Higher Rademacher Symbols","authors":"W. Duke","doi":"10.1080/10586458.2023.2219071","DOIUrl":"https://doi.org/10.1080/10586458.2023.2219071","url":null,"abstract":". Certain higher Rademacher symbols are defined that give class functions on the modular group. Their basic properties are derived via a two-variable reformulation of Eichler-Shimura cohomology. This reformulation better explains the role of cycle integrals and leads to new evaluations. The Rademacher symbols determine the values at non-positive integers of the zeta function for a narrow ideal class of a real quadratic field. This result is equivalent to one of Siegel, but is proven in a new way by using an identity for the value of such a zeta function at a positive integer greater than one as a sum of certain double zeta values defined for the quadratic field.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-15DOI: 10.1080/10586458.2023.2221866
Debanjana Kundu, L. Washington
{"title":"Heuristics for Anti-cyclotomic ℤp-extensions","authors":"Debanjana Kundu, L. Washington","doi":"10.1080/10586458.2023.2221866","DOIUrl":"https://doi.org/10.1080/10586458.2023.2221866","url":null,"abstract":"","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44458676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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