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- Jonsson, Jakob
(författare)
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On the 3-Torsion Part of the Homology of the Chessboard Complex
- 2010
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Ingår i: Annals of Combinatorics. - : Springer Science and Business Media LLC. - 0218-0006 .- 0219-3094. ; 14:4, s. 487-505
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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