The flag f-vectors of Gorenstein* order complexes of dimension 3
Satoshi Murai, Eran Nevo
TL;DR
This paper characterizes the cd-indices and f-vectors of Gorenstein* order complexes of dimensions 3 and 4, revealing a deep connection with flag homology spheres and advancing combinatorial understanding of these structures.
Contribution
It provides the first complete characterization of the cd-indices of Gorenstein* posets of rank 5 and the f-vectors of Gorenstein* order complexes in dimensions 3 and 4.
Findings
Characterization of cd-indices for Gorenstein* posets of rank 5
Complete description of f-vectors for Gorenstein* complexes in dimensions 3 and 4
Revealed connection between f-vectors of flag homology spheres and Gorenstein* complexes
Abstract
We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f-vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f-vectors of Gorenstein* order complexes in dimensions 3 and 4. This characterization rise a speculated intimate connection between the f-vectors of flag homology spheres and the f-vectors of Gorenstein* order complexes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications