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g-Elements, finite buildings and higher Cohen–Macaulay connectivity

Swartz, Ed

Journal of combinatorial theory. Series A, 2006-10, Vol.113 (7), p.1305-1320 [Periódico revisado por pares]

Elsevier Inc

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  • Título:
    g-Elements, finite buildings and higher Cohen–Macaulay connectivity
  • Autor: Swartz, Ed
  • Assuntos: Building ; Convex ear decomposition ; Doubly Cohen–Macaulay ; Face ring (Stanley–Reisner ring) ; g-Element ; h-Vector ; Weak order
  • É parte de: Journal of combinatorial theory. Series A, 2006-10, Vol.113 (7), p.1305-1320
  • Descrição: Chari proved that if Δ is a ( d − 1 ) -dimensional simplicial complex with a convex ear decomposition, then h 0 ⩽ ⋯ ⩽ h ⌊ d / 2 ⌋ [M.K. Chari, Two decompositions in topological combinatorics with applications to matroid complexes, Trans. Amer. Math. Soc. 349 (1997) 3925–3943]. Nyman and Swartz raised the problem of whether or not the corresponding g-vector is an M-vector [K. Nyman, E. Swartz, Inequalities for h- and flag h-vectors of geometric lattices, Discrete Comput. Geom. 32 (2004) 533–548]. This is proved to be true by showing that the set of pairs ( ω , Θ ) , where Θ is a l.s.o.p. for k [ Δ ] , the face ring of Δ, and ω is a g-element for k [ Δ ] / Θ , is nonempty whenever the characteristic of k is zero. Finite buildings have a convex ear decomposition. These decompositions point to inequalities on the flag h-vector of such spaces similar in spirit to those examined in [K. Nyman, E. Swartz, Inequalities for h- and flag h-vectors of geometric lattices, Discrete Comput. Geom. 32 (2004) 533–548] for order complexes of geometric lattices. This also leads to connections between higher Cohen–Macaulay connectivity and conditions which insure that h 0 < ⋯ < h i for a predetermined i.
  • Editor: Elsevier Inc
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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