We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n]. We show that the flag simplicial complex on ( [n] k ) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product [k]× [n− k] of two chains, and it is the join of a simplex and a sphere (that is, it is a Gorenstei...

A total order of the facets of a polytope is a geometric shelling if there exists a combinatorially equivalent polytope in which the corresponding order of facets becomes a line shelling. The subject of this paper is (geometric) shellings of 3-polytopes. Recently, a graph theoretical characterization of geometric shellings of 3-polytopes were given by Holt & Klee and Mihalisin & Klee. We rst gi...

Facet-defining inequalities of the symmetric traveling salesman problem (TSP) polytope play a prominent role in both polyhedral TSP research and state-of-the-art solvers. In this paper, we introduce new class facet-defining inequalities, circlet inequalities. These were first conjectured Gutekunst Williamson [Gutekunst SC, DP (2019) Characterizing integrality gap subtour LP for circulant proble...