Face vectors of flag complexes
Andrew Frohmader
TL;DR
This paper verifies a conjecture by Kalai and Eckhoff that the face vector of any flag complex can be realized as the face vector of a specific balanced complex, advancing understanding of face vector relationships.
Contribution
It proves the conjecture that the face vector of an arbitrary flag complex matches that of a particular balanced complex.
Findings
Confirmed the conjecture for all flag complexes
Established a link between flag complexes and balanced complexes
Enhanced understanding of face vector structures in combinatorial topology
Abstract
A conjecture of Kalai and Eckhoff that the face vector of an arbitrary flag complex is also the face vector of some particular balanced complex is verified.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models