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More Torsion in the Homology of the Matching ComplexPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### Place, publisher, year, edition, pages

2010. Vol. 19, no 3, 363-383 p.
##### Keyword [en]

Matching complex, simplicial homology torsion subgroup
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-27086ISI: 000283979400008Scopus ID: 2-s2.0-79952179731OAI: oai:DiVA.org:kth-27086DiVA: diva2:376229
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt434",{id:"formSmash:j_idt434",widgetVar:"widget_formSmash_j_idt434",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt440",{id:"formSmash:j_idt440",widgetVar:"widget_formSmash_j_idt440",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true});
##### Note

QC 20101210Available from: 2010-12-10 Created: 2010-12-06 Last updated: 2017-12-11Bibliographically approved

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.

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