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More Torsion in the Homology of the Matching Complex
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2010 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 19, no 3, 363-383 p.Article in journal (Refereed) Published
Abstract [en]

A matching on a set X is a collection of pairwise disjoint subsets of X of size two Using computers, we analyze the integral homology of the matching complex M, which is the simplicial complex of matchings on the set {1, ,n} The main result is the detection of elements of order p in the homology for p is an element of {5, 7, 11, 13} Specifically, we show that there are elements of order 5 in the homology of M-n for n >= 18 and for n is an element of {14, 16} The only previously known value was n = 14, and in this particular case we have a new computer-free proof Moreover, we show that there are elements of order 7 in the homology of M-n for all odd a between 23 and 41 and for n = 30 In addition, there are elements of order 11 in the homology of M-47 and elements of order 13 in the homology of M-62 Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of (H) over tilde (d)(M-n, Z) for 13 <= n <= 16, a complete description of the homology already exists for n <= 12 To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of M-n obtained by letting certain groups act on the chain complex.

Place, publisher, year, edition, pages
2010. Vol. 19, no 3, 363-383 p.
Keyword [en]
Matching complex, simplicial homology torsion subgroup
National Category
URN: urn:nbn:se:kth:diva-27086ISI: 000283979400008ScopusID: 2-s2.0-79952179731OAI: diva2:376229
QC 20101210Available from: 2010-12-10 Created: 2010-12-06 Last updated: 2010-12-10Bibliographically approved

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Jonsson, Jakob
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