Hilbert function and facet ideals of products of simplicial complexes

Nazeran Idrees () and Hafiza Nimra Nawaz ()
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Nazeran Idrees: Government College University
Hafiza Nimra Nawaz: Government College University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 787-798

Abstract: Abstract Aim of the article is to construct new simplicial complexes by generalizing the idea of graph operations for simplicial complexes. Union, join, corona product, cartesian product, tensor product and strong product of two simplicial complexes are defined. F-vectors of the product complexes are computed in terms of their component simplicial complexes. Hilbert function and facet ideals of these product complexes are also computed and relations of these invarinats with that of their component simplicial complexes is established. Moreover, interrelation between these products is also established in terms of Hilbert function.

Keywords: Simplicial complex; Graph operations; f-vector; Hilbert function; Stanley-Reisner ideal; Facet ideal (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00147-z

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