4 papers
Local Shellings of Broken-Circuit Complexes via Boundary States and the Chromatic Specialization of the Negami Polynomial
Iwao Mizukai
For edge-disjoint graphs meeting along a finite boundary, we construct relative shellings of NBC faces with prescribed boundary connectivity. The construction adds paths in spannin…
The Negami Polynomial and Broken-Circuit Stanley--Reisner Rings
Iwao Mizukai
We summarize the classical passage from the chromatic specialization of Negami's polynomial to the Hilbert series of a broken-circuit Stanley--Reisner ring, and record formulas for…
A Categorical Framework for the Negami Polynomial and Its Splitting Formula
Iwao Mizukai
I give an elementary categorical lift of the three-variable Negami polynomial and of the boundary state structure underlying the splitting formula.
Ollivier Ricci curvature of Cayley graphs for dihedral groups, generalized quaternion groups, and cyclic groups
Iwao Mizukai, Akifumi Sako
Lin, Lu, and Yau formulated the Ricci curvature of edges in simple undirected graphs[2]. Using their formulations, we calculate the Ricci curvatures of Cayley graphs for the dihedr…