Regularity and $h$-Polynomials of Edge Ideals
Copyright policy )Regularity and $h$-Polynomials of Edge Ideals
For any two integers $d,r \geqslant 1$, we show that there exists an edge ideal $I(G)$ such that ${\rm reg}\left(R/I(G)\right)$, the Castelnuovo-Mumford regularity of $R/I(G)$, is $r$, and $\deg h_{R/I(G)}(t)$, the degree of the $h$-polynomial of $R/I(G)$, is $d$. Additionally, if $G$ is a graph on $n$ vertices, we show that ${\rm reg}\left(R/I(G)\right) + \deg h_{R/I(G)}(t) \leqslant n$.
- Osaka University Japan
- McMaster University Canada
- Kitami Institute of Technology Japan
Commutative rings defined by binomial ideals, toric rings, etc., Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, 13D02, 13D40, 05C69, 05C70, 05E40, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Combinatorial aspects of commutative algebra, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Commutative rings defined by binomial ideals, toric rings, etc., Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, 13D02, 13D40, 05C69, 05C70, 05E40, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Combinatorial aspects of commutative algebra, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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