Enumeration of plane partitions by descents

2019/11/08 by Yeliussizov, Damir · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.03259

Abstract

We study certain bijection between plane partitions and ℕ-matrices. As applications, we prove a Cauchy-type identity for generalized dual Grothendieck polynomials. We introduce two statistics on plane partitions, whose generating functions are similar to classical MacMahon's formulas; one of these statistics is equidistributed with the usual volume. We also show natural connections with the longest increasing subsequences of words.

Cited by

• Flagged Hamel--Goulden formulas
• Inhomogeneous q-Whittaker Polynomials I: Duality and Expansions

Related

• MacMahon's statistics on higher-dimensional partitions
• Two formulas for plane paritions
• Plane Partition Polynomial Asymptotics
• A simple bijection between permutation matrices and descending plane partitions without special parts
• A bijective proof of the Cauchy identity for Grothendieck polynomials