The \(r\)-multipermutations
type: Item
instance of: scholarly article
title: The \(r\)-multipermutations
zbMATH Open document ID: 0804.05001
DOI: 10.1016/0097-3165(94)90003-5
author: Seung Kyung Park
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-11-21T00:00:00Z
review text: This paper deals with the counting techniques on certain kind of permutations, called \(r\)-multipermutations, on the multiset \(\{1^ r, 2^ r, \dots, n^ r\}\). A multiset is a set with possibly repeated elements and is formally defined as an ordered pair \((S,F)\), \(S\) being a set (say) \(\{m_ 1, \dots, m_ r\}\) and \(f\) a function from \(S\) to the set of nonnegative integers, and is written as \(\{m_ 1^{f(m_ 1)}, \dots, m_ r^{f(m_ r)}\}\). An \(r\)-multipermutation of the set \(\{m_ 1, \dots, m_ n\}\) is a permutation \(a_ 1, a_ 2, \dots, a_{rn}\) of the multiset \(\{m^ r_ 1, m_ 2^ r, \dots, m^ r_ n\}\), where if \(i<j<k\) and \(a_ i = a_ k\) then \(a_ j \geq a_ i\). Rather than considering \(S = \{m_ 1, m_ 2, \dots, m_ n\}\), the set considered here is \(\{1,2, \dots, n\} = [n]\), and the multiset is then \(\{1^ r, 2^ r, \dots, n^ r\} = [n]^{(r)}\). Various interesting results dealing with the counting of such \(r\)-multipermutations by inversions, major index, descents, and left-right minima are derived.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 617608
zbMATH Keywords: \(r\)-multipermutations
zbMATH Keywords: counting
zbMATH Keywords: permutations
zbMATH Keywords: multiset
reviewed by: D. V. Chopra
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90003-5
OpenAlex ID: W1978349579
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description: scientific article; zbMATH DE number 617608