Pub Date : 2024-04-08DOI: 10.1080/10586458.2024.2334381
Dazhao Tang
Let pod−k(n) denote the number of partition k-tuples of n where the odd parts in each partition are distinct. By utilizing some q-series manipulations and iterative computations, we derive dozens ...
让 pod-k(n)表示 n 的分区 k 元组数，其中每个分区的奇数部分都是不同的。通过利用一些 q 序列操作和迭代计算，我们得出了几十个 ...
{"title":"Internal Congruences Modulo Powers of 5 for Partition k-Tuples with Odd Parts Distinct","authors":"Dazhao Tang","doi":"10.1080/10586458.2024.2334381","DOIUrl":"https://doi.org/10.1080/10586458.2024.2334381","url":null,"abstract":"Let pod−k(n) denote the number of partition k-tuples of n where the odd parts in each partition are distinct. By utilizing some q-series manipulations and iterative computations, we derive dozens ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587613","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 : 2024-04-04DOI: 10.1080/10586458.2024.2337910
J. D. Mireles James, Francis C. Motta, Vincent Naudot
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations w...
{"title":"State Dependent Delay Maps: Numerical Algorithms and Dynamics of Projections","authors":"J. D. Mireles James, Francis C. Motta, Vincent Naudot","doi":"10.1080/10586458.2024.2337910","DOIUrl":"https://doi.org/10.1080/10586458.2024.2337910","url":null,"abstract":"This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations w...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602543","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 : 2024-04-03DOI: 10.1080/10586458.2024.2334378
Alexander R. Klotz, Caleb J. Anderson
The ropelength of a knot is the minimum length required to tie it. Computational upper bounds have previously been computed for every prime knot with up to 11 crossings. Here, we present ropelength...
{"title":"Ropelength and Writhe Quantization of 12-Crossing Knots","authors":"Alexander R. Klotz, Caleb J. Anderson","doi":"10.1080/10586458.2024.2334378","DOIUrl":"https://doi.org/10.1080/10586458.2024.2334378","url":null,"abstract":"The ropelength of a knot is the minimum length required to tie it. Computational upper bounds have previously been computed for every prime knot with up to 11 crossings. Here, we present ropelength...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578546","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 : 2024-04-03DOI: 10.1080/10586458.2024.2333722
Marek Kaluba, Piotr Mizerka, Piotr W. Nowak
We show that the cohomological Laplacian in degree 1 in the group cohomology of SL3(Z) is a sum of hermitian squares in the algebra Mn(RG). We provide an estimate of the spectral gap for this Lapla...
{"title":"Spectral Gap for the Cohomological Laplacian of SL3(ℤ)","authors":"Marek Kaluba, Piotr Mizerka, Piotr W. Nowak","doi":"10.1080/10586458.2024.2333722","DOIUrl":"https://doi.org/10.1080/10586458.2024.2333722","url":null,"abstract":"We show that the cohomological Laplacian in degree 1 in the group cohomology of SL3(Z) is a sum of hermitian squares in the algebra Mn(RG). We provide an estimate of the spectral gap for this Lapla...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587834","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 : 2024-04-02DOI: 10.1080/10586458.2024.2334379
Rangel Hernández-Ortiz, Kolja Knauer, Luis Pedro Montejano, Manfred Scheucher
J.-P. Roudneff conjectured in 1991 that every arrangement of n≥2d+1≥5 pseudohyperplanes in the real projective space Pd has at most ∑i=0d−2(n−1i) complete cells (i.e., cells bounded by each hyperpl...
{"title":"Roudneff’s Conjecture in Dimension 4","authors":"Rangel Hernández-Ortiz, Kolja Knauer, Luis Pedro Montejano, Manfred Scheucher","doi":"10.1080/10586458.2024.2334379","DOIUrl":"https://doi.org/10.1080/10586458.2024.2334379","url":null,"abstract":"J.-P. Roudneff conjectured in 1991 that every arrangement of n≥2d+1≥5 pseudohyperplanes in the real projective space Pd has at most ∑i=0d−2(n−1i) complete cells (i.e., cells bounded by each hyperpl...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578889","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 : 2024-03-12DOI: 10.1080/10586458.2024.2309507
Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison
We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson’...
{"title":"Coxeter Quotients of Knot Groups through 16 Crossings","authors":"Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison","doi":"10.1080/10586458.2024.2309507","DOIUrl":"https://doi.org/10.1080/10586458.2024.2309507","url":null,"abstract":"We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson’...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149093","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 : 2024-02-11DOI: 10.1080/10586458.2024.2308246
Mary Barker, Benjamin Standaert, Ben Wormleighton
The McKay correspondence has had much success in studying resolutions of 3-fold quotient singularities through a wide range of tools coming from geometry, combinatorics, and representation theory. ...
{"title":"Crepant Resolutions, Mutations, and the Space of Potentials","authors":"Mary Barker, Benjamin Standaert, Ben Wormleighton","doi":"10.1080/10586458.2024.2308246","DOIUrl":"https://doi.org/10.1080/10586458.2024.2308246","url":null,"abstract":"The McKay correspondence has had much success in studying resolutions of 3-fold quotient singularities through a wide range of tools coming from geometry, combinatorics, and representation theory. ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757063","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 : 2024-02-01DOI: 10.1080/10586458.2024.2309517
Cristina Bertone, Francesca Cioffi, Matthias Orth, Werner M. Seiler
We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods for the study of Hi...
我们介绍了准稳定理想上的相对标记基础的概念，以及构造方法和函数解释，为研究Hi...
{"title":"Open Covers and Lex Points of Hilbert Schemes Over Quotient Rings via Relative Marked Bases","authors":"Cristina Bertone, Francesca Cioffi, Matthias Orth, Werner M. Seiler","doi":"10.1080/10586458.2024.2309517","DOIUrl":"https://doi.org/10.1080/10586458.2024.2309517","url":null,"abstract":"We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods for the study of Hi...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756855","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 : 2024-01-07DOI: 10.1080/10586458.2023.2300412
Alex Chandler, Eugene Gorsky
We study the structure of triply graded Khovanov-Rozansky homology using both the data recently computed by Nakagane and Sano for knots up to 11 crossings, and the sl(2) action defined by the secon...
{"title":"Structures in HOMFLY-PT Homology","authors":"Alex Chandler, Eugene Gorsky","doi":"10.1080/10586458.2023.2300412","DOIUrl":"https://doi.org/10.1080/10586458.2023.2300412","url":null,"abstract":"We study the structure of triply graded Khovanov-Rozansky homology using both the data recently computed by Nakagane and Sano for knots up to 11 crossings, and the sl(2) action defined by the secon...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139398010","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 : 2024-01-04DOI: 10.1080/10586458.2023.2300432
John Chae
This is a companion paper to earlier work of the author, which generalizes to an infinite family of (2,2w+1)-cabling of the figure eight knot (|w|>3) and proposes general formulas for the two-varia...
{"title":"A Cable Knot and BPS-Series II","authors":"John Chae","doi":"10.1080/10586458.2023.2300432","DOIUrl":"https://doi.org/10.1080/10586458.2023.2300432","url":null,"abstract":"This is a companion paper to earlier work of the author, which generalizes to an infinite family of (2,2w+1)-cabling of the figure eight knot (|w|>3) and proposes general formulas for the two-varia...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463846","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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