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On the 3-Torsion Part of the Homology of the Chessboard Complex
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 14, no 4, 487-505 p.Article in journal (Refereed) Published
Abstract [en]

Let 1 (d) (M-m,M-n; Z) not equal 0. Second, for each k >= 0, we show that there is a polynomial f(k)(a, b) of degree 3k such that the dimension of (H) over tilde (k+a+2b-2) (M-k+a+3b-1,M- k+2a+3b-1; Z(3)), viewed as a vector space over Z(3), is at most f(k)(a, b) for all a >= 0 and b >= k+ 2. Third, we give a computer- free proof that (H) over tilde (2) (M-5,M-5; Z) congruent to Z(3). Several proofs are based on a new long exact sequence relating the homology of a certain subcomplex of M-m,M-n to the homology of M-m-2,M-n-1 and M-m-2,M-n-3.

Place, publisher, year, edition, pages
2010. Vol. 14, no 4, 487-505 p.
Keyword [en]
matching complex, chessboard complex, simplicial homology
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-36258DOI: 10.1007/s00026-011-0073-xISI: 000292037700007ScopusID: 2-s2.0-79952705706OAI: diva2:430478
QC 20110711Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2011-07-11Bibliographically approved

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