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Hilbert function and facet ideals of products of simplicial complexes

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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.

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Authors and Affiliations

  1. Department of Mathematics, Government College University, Faisalabad, Pakistan

    Nazeran Idrees & Hafiza Nimra Nawaz

Authors
  1. Nazeran Idrees
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  2. Hafiza Nimra Nawaz
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Correspondence to Nazeran Idrees.

Additional information

Communicated by Jugal K Verma.

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Idrees, N., Nawaz, H.N. Hilbert function and facet ideals of products of simplicial complexes. Indian J Pure Appl Math 52, 787–798 (2021). https://doi.org/10.1007/s13226-021-00147-z

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  • DOI: https://doi.org/10.1007/s13226-021-00147-z

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