Journal article
The Elser nuclei sum revisited
DMTCS Proceedings, v 23(1), dmtcs:7012
01 May 2021
Abstract
Fix a finite undirected graph [GAMMA] and a vertex v of [GAMMA] . Let E be the set of edges of [GAMMA]. We call a subset F of E pandemic if each edge of [GAMMA] has at least one endpoint that can be connected to v by an F-path (i.e., a path using edges from F only). In 1984, Elser showed that the sum of [(-1).sup.|F|] over all pandemic subsets F of E is 0 if E [not equal to] [empty set]. We give a simple proof of this result via a sign-reversing involution, and discuss variants, generalizations and a refinement using discrete Morse theory. Keywords: graph, simplicial complex, alternating sum, discrete Morse theory
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2 citations in Scopus
Details
- Title
- The Elser nuclei sum revisited
- Creators
- Darij Grinberg - Drexel University
- Publication Details
- DMTCS Proceedings, v 23(1), dmtcs:7012
- Publisher
- DMTCS
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Scopus ID
- 2-s2.0-85116033561
- Other Identifier
- 991019170488804721