Özet:

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.

Anahtar Kelimeler: