{"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}
{"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}
{"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}
{"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}
{"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}
Chris Anderson, Kenneth L. Baker, Xinghua Gao, Marc Kegel, Khanh Le, Kyle Miller, Sinem Onaran, Geoffrey Sangston, Samuel Tripp, Adam Wood, Ana Wright
{"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}
{"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}
{"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}
{"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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