Involutions under Bruhat order and labeled Motzkin Paths

Autor:	Michael Coopman, Zachary Hamaker
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	05A19 Mathematics::Combinatorics FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Combinatorics (math.CO)
Popis:	In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a recently introduced interpretation of this rank generating function in terms of visible inversions. By restricting our identity to fixed-point-free (FPF) involutions, we recover an identity due to Louis Billera, Lionel Levine and Karola M\'esz\'aros with a previous bijective proof by Matthew Watson. Our work sheds new light on the Ethiopian dinner game. Comment: 7 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::319794d78fae6f12a5c6fe8a146dace3 http://arxiv.org/abs/2106.06021 Zobrazit plný text záznamu