Generalized Euler and Chu-Vandermonde identities
type: Item
instance of: scholarly article
title: Generalized Euler and Chu-Vandermonde identities
zbMATH Open document ID: 0602.05008
DOI: 10.1016/0097-3165(86)90022-1
author: Kung-Wei Yang
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: The object of this paper is to present two surprisingly general identities involving the generating functions of the number of inversions between multisets (of not necessarily uniform multiplicities). The first identity is a generalization of the Chu-Vandermonde identity, and the second a well-known identity of Euler. Our proofs are based on a one-to- one correspondence between multisubsets and certain permissible paths in a digraph with monomial weights.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3970757
zbMATH Keywords: Euler identity
zbMATH Keywords: identities
zbMATH Keywords: generating functions
zbMATH Keywords: Chu-Vandermonde identity
zbMATH Keywords: paths
zbMATH Keywords: digraph
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90022-1
OpenAlex ID: W1967414557
cites work: Q4146776
cites work: Q4769056
cites work: On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions
cites work: On the number of certain lattice polygons
cites work: A q-Polynomial Identity
description: scientific article; zbMATH DE number 3970757