On sums over partially ordered sets
type: Item
instance of: scholarly article
title: On sums over partially ordered sets
zbMATH Open document ID: 0936.06001
author: Klaus Dohmen
published in: The Electronic Journal of Combinatorics
publication date: 2000-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/120223
full work available at URL: v6i1r34.html
review text: The author establishes a general theorem for reducing sums of type \(\sum_{y\geq x}g(y)\), where \(g\) is a mapping from a partially ordered set into an abelian group. The result is applied to deduce the known result of G.-C. Rota, as well as of \textit{A. Blass} and \textit{B. E. Sagan} [Adv. Math. 127, No. 1, 94-123 (1997; Zbl 0872.06004)] on the Möbius function, to improve the inclusion-exclusion principle (see also the author [Arch. Math. 72, No. 4, 298-303 (1999; Zbl 0934.05011)]), and to obtain some conclusions about the Tutte polynomial and Crapo's beta invariant in matroid theory.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 1345964
zbMATH Keywords: partially ordered set
zbMATH Keywords: Möbius function
zbMATH Keywords: inclusion-exclusion principle
zbMATH Keywords: Tutte polynomial
zbMATH Keywords: matroid
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1345964