The e-vector of a simplicial complex

2018/06/13 by Wayne A. Johnson, Johnson, Wayne A., Wiktor J. Mogilski +1
Computer Science · Mathematics · #05E45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1806.05239

openalex publication_date 2018/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, Δ, and we introduce the e-vector of Δ, which relates to the coefficients of the exponential Hilbert series. We explore the relationship of the e-vector with the classical f-vector and h-vector of Δ while simultaneously investigating the geometric information that the e-vector encodes about Δ. We then prove a simple combinatorial identity for the e-vector in the case where Δ is an Eulerian manifold.

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