There is a long history of constructions of non-shellable triangulations of -dimensional (topological) balls. This paper gives a survey of these constructions, including Furch’s 1924 construction using knotted curves, which also appears in Bing’s 1962 survey of combinatorial approaches to the Poincaré conjecture, Newman’s 1926 explicit example, and M. E. Rudin’s 1958 non-shellable triangulation...

A generalized convex shelling was introduced by Kashiwabara, Nakamura & Okamoto for their representation theorem of convex geometries. Motivated by the work by Edelman & Reiner, we study local topology of the free complex of a two-dimensional separable generalized convex shelling. As a result, we prove a deletion of an element from such a complex is homotopy equivalent to a single point or two ...

This note defines a flag vector for i-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author’s On quantum topology, hypergraphs and flag vectors, (preprint q-alg/9708001). The purpose of this note is to state concisely a new combinatorial concept. This note is an an...

We prove the equivalence of EL-shellability and existence recursive atom ordering independent roots. show that a comodernistic lattice, as defined by Schweig Woodroofe, admits roots, therefore is EL-shellable. also present discuss simpler EL-shelling on one most important classes order congruence lattices.