Carptopus

Triangle Sums, Peripheral Cycles, and Contractions for Orderable Cographic Matroids

For closed simplicial surface triangulations, this preprint proves a general triangle-rooted gluing theorem for compatible cographic orderings and an exact if-and-only-if criterion for triangle sums. It constructs infinite families of 3-connected regular non-graphic orderable cog...

Log-concavity of Reduced Composition Polynomials via Adjacent B-spline Refinement Columns

Ardila and Doker associated a reduced composition polynomial f_c(q) with every positive integer composition c and asked whether its coefficient sequence is unimodal or, more strongly, log-concave. We prove that the coefficient sequence is log-concave for every positive integer co...

Triangle Sums, Peripheral Cycles, and Contractions for Orderable Cographic Matroids

For closed simplicial surface triangulations, this preprint proves a general triangle-rooted gluing theorem for compatible cographic orderings and an exact if-and-only-if criterion for triangle sums. It constructs infinite families of 3-connected regular non-graphic orderable cog...

Log-concavity of Reduced Composition Polynomials via Adjacent B-spline Refinement Columns

Ardila and Doker associated a reduced composition polynomial f_c(q) with every positive integer composition c and asked whether its coefficient sequence is unimodal or, more strongly, log-concave. We prove that the coefficient sequence is log-concave for every positive integer co...

Every Two-Vertex Premaniplex Is the Symmetry Type Graph of a Finite Abstract Polytope

For every rank r>=3, there are 2^r-1 connected two-vertex premaniplexes. We prove that every one of them is the full symmetry type graph of a finite abstract polytope. The main argument localizes the support of the recursive regular-polytopal voltage construction, treats arbitrar...