Algebraic shifting of strongly edge decomposable spheres

2007/09/28 by Satoshi Murai, Murai, Satoshi · 3 citations
Mathematics · #13F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.CO #msc:13F55

paper · pdf · doi:10.48550/arxiv.0709.4518

19 pages. Add a few examples in the Introduction. To appear in J. Combin. Theory Ser. A

openalex publication_date 2007/09/28 · arxiv created 2009/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Nevo introduced the notion of strongly edge decomposable spheres. In this paper, we characterize the algebraic shifted complex of those spheres. Algebraically, this result yields the characterization of the generic initial ideal of the Stanley--Reisner ideal of Gorenstein* complexes having the strong Lefschetz property in characteristic 0.

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• On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders
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