M.L. Wachs, Whitney homology of semipure shellable posets, J. Algebraic Combin. 9 (1999), 173--207. Home/Search Document Details and Download
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Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial.. - Duval (1996) (4 citations) (Correct)
....layer, the subcomplex of all faces of K whosedegreeisatleastr 1 (equivalently, the subcomplex generated by all facets whose dimension is at least r) and K [i] K (i,i) thepure i skeleton, the pure subcomplex generated by all i dimensional faces. The notation K [i] is due to Wachs [Wa]. Other interpretations of K (r,s) then, are that K (r,s) K r ) s) and, if r # s,thatK (r,s) K [r] s) Lemma 2.1. Let L # K be a pair of simplicial complexes. a) If deg L # i 1, then L # K i . b) L i # K i . Proof. a) Let F # L.Becausedeg L ....
....of combinatorics 3 (1996) #R21 7 If i d 1, then K [i 1] and K [i] are Cohen Macaulay. In that case, K [i 1] i) is the skeleton of a Cohen Macaulay complex, and hence Cohen Macaulay. Then, by Corollary 3.2, # i (K) K [i] K [i 1] i) is relative Cohen Macaulay. See [Wa] for another characterization of sequential Cohen Macaulayness, which relies upon Theorem 3.3. 4 Algebraic shifting Algebraic shifting transforms a simplicial complex into a shifted simplicial complex with the same f vector, and also preserves many algebraic properties of the original complex. ....
M. Wachs, "Whitney homology of semipure shellable posets," preprint, 1996.
Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial.. - Duval (1996) (4 citations) (Correct)
....layer, the subcomplex of all faces of K whose degree is at least r 1 (equivalently, the subcomplex generated by all facets whose dimension is at least r) and K [i] K (i;i) the pure i skeleton, the pure subcomplex generated by all i dimensional faces. The notation K [i] is due to Wachs [Wa]. Other interpretations of K (r;s) then, are that K (r;s) K r ) s) and, if r s, that K (r;s) K [r] s) Lemma 2.1. Let L K be a pair of simplicial complexes. a) If deg L i 1, then L K i . b) L i K i . Proof. a) Let F 2 L. Because deg L F i ....
....3 (1996) #R21 7 If i d Gamma 1, then K [i 1] and K [i] are Cohen Macaulay. In that case, K [i 1] i) is the skeleton of a Cohen Macaulay complex, and hence Cohen Macaulay. Then, by Corollary 3.2, Omega i (K) K [i] K [i 1] i) is relative Cohen Macaulay. See [Wa] for another characterization of sequential Cohen Macaulayness, which relies upon Theorem 3.3. 4 Algebraic shifting Algebraic shifting transforms a simplicial complex into a shifted simplicial complex with the same f vector, and also preserves many algebraic properties of the original complex. ....
M. Wachs, "Whitney homology of semipure shellable posets," preprint, 1996.
Topology of Matching, Chessboard, and General Bounded Degree Graph .. - Wachs Self-citation (Wachs) (Correct)
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M.L. Wachs, Whitney homology of semipure shellable posets, J. Algebraic Combin. 9 (1999), 173--207.
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