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dc.contributor.authorGrinberg, Darij
dc.date.accessioned2021-03-16T14:45:18Z
dc.date.available2021-03-16T14:45:18Z
dc.date.issued2021-03-16
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3846
dc.description.abstractFix 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 $E$ $\textit{pandemic}$ 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 $\left(-1\right)^{\left| F\right|}$ over all pandemic subsets $F$ of $E$ is $0$ if $E\neq\varnothing$. We give a simple proof of this result via a sign-reversing involution, and discuss variants, generalizations and a refinement using discrete Morse theory.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2021-05
dc.subjectGraph theoryen_US
dc.subjectNucleien_US
dc.subjectSimplicial complexen_US
dc.subjectDiscrete Morse theoryen_US
dc.subjectAlternating sumen_US
dc.subjectEnumerative combinatoricsen_US
dc.subjectInclusion/ exclusionen_US
dc.subjectConvexityen_US
dc.titleThe Elser Nuclei Sum Revisiteden_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2021-05
local.scientificprogramOWLF 2020en_US
local.series.idOWP-2021-05en_US
dc.identifier.urnurn:nbn:de:101:1-2021031910294725471725
dc.identifier.ppn1752185447


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