Mathematics Seminar
Date: Wednesday, 13 August 2025
Time: 2.00 - 3.00 PM
Venue: Lecture Hall 1
Stanley-Reisner ideals of higher independence complexes of chordal graphs
Amit Roy
Chennai Mathematical Institute.
13-08-25

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Abstract

For t ≥ 2, the t-independence complex Indt(G) of a graph G is the collection of all A ⊆ V (G) such that each connected component of the induced subgraph G[A] has at most t − 1 vertices. For t = 2, the t-independence complex is the well-known independence complex of a graph. In this talk, we consider the Stanley-Reisner ideal It(G) of Indt(G) for a general t and discuss some of its algebraic properties. In particular, we see that for a chordal graph G and for all t ≥ 2 reg(R/It(G)) = (t − 1)νt(G) and pd(R/It(G)) = bight(It(G)), where νt(G) denotes the induced matching number of the corresponding hypergraph of It(G), and reg, pd, and bight stand for the regularity, projective dimension, and big height, respectively.