On the 3-Torsion Part of the Homology of the Chessboard Complex
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
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.
matching complex, chessboard complex, simplicial homology
IdentifiersURN: urn:nbn:se:kth:diva-36258DOI: 10.1007/s00026-011-0073-xISI: 000292037700007ScopusID: 2-s2.0-79952705706OAI: oai:DiVA.org:kth-36258DiVA: diva2:430478
QC 201107112011-07-112011-07-112011-07-11Bibliographically approved