Face-Counting Identities and Derivatives of Face Polynomials

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Turkish Journal of Mathematics and Computer Science
Volume:15 Issue:2
Face-Counting Identities and Derivatives of Face Polynomials

Face-Counting Identities and Derivatives of Face Polynomials

Authors : Hossein Teimoori Faal

Pages : 443-448

Doi:10.47000/tjmcs.1120399

View : 27 | Download : 30

Publication Date : 2023-12-31

Article Type : Research Paper

Abstract :In this paper, we first introduce two incidence matrices related to the vertex-deck and the edge-deck of a given simplicial complex. Then, we obtain two face-counting identities based on these incidence matrices. Using these face-counting identities, we present combinatorial interpretations of the first and the second derivatives of face polynomials of simplicial complexes. We also propose several interesting open questions and conjectures. Finally, we conclude the paper with a discussion about some possible future research works.
Keywords : Face polynomial, face counting identities, incidence matrices, derivatives

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