Bijection between bigrassmannian permutations maximal below a permutation and its essential set
type: Item
instance of: scholarly article
title: Bijection between bigrassmannian permutations maximal below a permutation and its essential set
zbMATH Open document ID: 1188.05002
author: Masato Kobayashi
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/229998
full work available at URL: v17i1n27.html
review text: Summary: Bigrassmannian permutations are known as permutations which have precisely one left descent and one right descent. They play an important role in the study of Bruhat order. Fulton introduced the essential set of a permutation and studied its combinatorics. As a consequence of his work, it turns out that the essential set of bigrassmannian permutations consists of precisely one element. In this article, we generalize this observation for essential sets of arbitrary permutations. Our main theorem says that there exists a bijection between bigrassmanian permutations maximal below a permutation and its essential set. For the proof, we make use of two equivalent characterizations of bigrassmannian permutations by Lascoux-Schützenberger and Reading.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 5721436
zbMATH Keywords: bigrassmanian permutations
zbMATH Keywords: Bruhat order
zbMATH Keywords: essential set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721436