5 papers · 1 filter
Poset Partitions and the Combinatorics of the -Index
Felipe Caster, Dan Guyer, José Alejandro Samper
We introduce a new class of Eulerian posets, called S-partitionable posets, which have a non-negative cd-index. These posets are a generalization of S-shellable complexes introduce…
Unbounded matroids
Jonah Berggren, Jeremy L. Martin, José A. Samper
A matroid base polytope is a polytope in which each vertex has 0,1 coordinates and each edge is parallel to a difference of two coordinate vectors. Matroid base polytopes are descr…
Discrete Curvatures and Convex Polytopes
Jesús A. De Loera, Jillian Eddy, Sawyer Jack Robertson +1
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere posi…
Hopf monoids of ordered simplicial complexes
Federico Castillo, Jeremy L. Martin, Jose A. Samper
We study pure ordered simplicial complexes (i.e., simplicial complexes with a linear order on their ground sets) from the Hopf-theoretic point of view. We define a \textit{Hopf cla…
The -index of semi-Eulerian posets
Martina Juhnke-Kubitzke, José Alejandro Samper, Lorenzo Venturello
We generalize the definition of the -index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficien…