Proof of a conjecture of Morales–Pak–Panova on reverse plane partitions

Autor:	Jack C. D. Zhao, Michael X.X. Zhong, Peter L. Guo
Rok vydání:	2019
Předmět:	Mathematics::Combinatorics Conjecture Plane (geometry) Applied Mathematics 010102 general mathematics Skew Generating function Hook length formula 01 natural sciences 010101 applied mathematics Combinatorics Equivariant cohomology Young tableau 0101 mathematics A determinant Mathematics
Zdroj:	Advances in Applied Mathematics. 108:45-66
ISSN:	0196-8858
DOI:	10.1016/j.aam.2019.03.005
Popis:	Using the equivariant cohomology theory, Naruse obtained a hook length formula for the number of standard Young tableaux of skew shape λ / μ . Morales, Pak and Panova found two q-analogues of Naruse's formula respectively by counting semistandard Young tableaux of shape λ / μ and reverse plane partitions of shape λ / μ . When λ and μ are both staircase shape partitions, Morales, Pak and Panova conjectured that the generating function of reverse plane partitions of shape λ / μ can be expressed as a determinant whose entries are related to q-analogues of the Euler numbers. The objective of this paper is to settle this conjecture.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::efdc42ff5e0ec75457e512c875a9d544 https://doi.org/10.1016/j.aam.2019.03.005 Zobrazit plný text záznamu Full Text from ScienceDirect