In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume.The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Les mer
ArticlesFrancois Bergeron, $(\operatorname {GL}_k \times \ \mathbb {S}_n)$-modules of multivariate diagonal harmonicsFrancesco Brenti, Some open problems on Coxeter groups and unimodalityR. Kenyon, Some combinatorial problems arising in the dimer modelPer Alexandersson and Valentin Feray, A positivity conjecture on the structure constants of shifted Jack functionsGreta Panova, Complexity and asymptotics of structure constantsJonathan Novak and Brendon Rhoades, Increasing subsequences and Kronecker coefficientsNathan Williams, Combinatorics and braid varietiesIsabella Novik and Hailun Zheng, Neighborly spheres and transversal numbersHugh Thomas, Realizing simplicial complexes as the boundary of the totally non-negative part of a varietySam Hopkins, Order polynomial product formulas and poset dynamicsThomas Lam, An invitation to positive geometriesSatoshi Murai, An upper bound problem for triangulations of manifoldsIgor Pak, What is a combinatorial interpretation?James Propp, Trimer covers in the triangular grid: Twenty mostly open problemsLaura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki, The mystery of plethysm coefficientsTri Lai, Problems in the enumeration of tilingsZhao Gao, Claudiu Raicu and Keller VandeBogert, Some questions arising from the study of cohomology on flag varietiesAlexander Yong, Castelnuovo-Mumford regularity and Schubert geometryRalf Schiffler, Perfect matching problems in cluster algebras and number theory
Les mer
Produktdetaljer
ISBN
9781470473334
Publisert
2024-10-31
Utgiver
Vendor
American Mathematical Society
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
371