Generalized multiplicities of edge ideals
Abstract
We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show the -multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the -multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs.
Cite
@article{arxiv.1607.00733,
title = {Generalized multiplicities of edge ideals},
author = {Ali Alilooee and Ivan Soprunov and Javid Validashti},
journal= {arXiv preprint arXiv:1607.00733},
year = {2020}
}
Comments
24 pages, 6 figures. The results of Theorem 4.6 and Theorem 9.2 are now more general. To appear in Journal of Algebraic Combinatorics