An interpretation for Garsia and Remmel's \(q\)-hit numbers
type: Item
instance of: scholarly article
title: An interpretation for Garsia and Remmel's \(q\)-hit numbers
zbMATH Open document ID: 0891.05008
author: Morris Dworkin
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-03-04T00:00:00Z
review text: Garsia and Remmel's \(q\)-analogue of the rook numbers and hit numbers associated with a Ferrers board is studied. A new recurrence for these \(q\)-hit numbers is found. Also, a statistic on permutations that constitutes a direct combinatorial interpretation of the \(q\)-hit numbers is defined. The statistic is used to prove a reciprocity theorem.
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1123556
zbMATH Keywords: \(q\)-analogue
zbMATH Keywords: rook numbers
zbMATH Keywords: hit numbers
zbMATH Keywords: Ferrers board
zbMATH Keywords: statistic
zbMATH Keywords: reciprocity theorem
reviewed by: G. Gutin
MaRDI profile type: Publication
full work available at URL: jcta.1997.2823
OpenAlex ID: W2001240420
cites work: Q4146776
cites work: A Combinatorial Property of q-Eulerian Numbers
cites work: The path-cycle symmetric function of a digraph
cites work: On the cover polynomial of a digraph
cites work: Q5620607
cites work: Recursive statistics on words
cites work: Q-counting rook configurations and a formula of Frobenius
cites work: Rook Theory. I.: Rook Equivalence of Ferrers Boards
cites work: Q3243274
cites work: Q3748279
DOI: 10.1006/JCTA.1997.2823
description: scientific article; zbMATH DE number 1123556