Homological connectivity of random k-dimensional complexes

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dc.creatorMeshulam, R.
dc.creatorWallach, N.
dc.date2006-09-27
dc.date.accessioned2026-07-07T07:25:20Z
dc.date.available2026-07-07T07:25:20Z
dc.descriptionLet Delta_{n-1} denote the (n-1)-dimensional simplex. Let Y be a random k-dimensional subcomplex of Delta_{n-1} obtained by starting with the full (k-1)-dimensional skeleton of Delta_{n-1} and then adding each k-simplex independently with probability p. Let H_{k-1}(Y;R) denote the (k-1)-dimensional reduced homology group of Y with coefficients in a finite abelian group R. Let R and k \geq 1 be fixed. It is shown that p=(k \log n)/n is a sharp threshold for the vanishing of H_{k-1}(Y;R).
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0609773
dc.identifierhttp://arxiv.org/abs/math/0609773
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116680
dc.subjectCombinatorics
dc.subject55U10 (Primary); 05C80 (Secondary)
dc.titleHomological connectivity of random k-dimensional complexes
dc.typetext

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