In this paper, we perform a systematic study of permutation statistics and bijective maps on
permutations in which we identify and prove 122 instances of the homomesy phenomenon …

Let F be a finite set of circles in the plane. The usual convex closure restricted to F yields a
convex geometry, which is a combinatorial structure introduced by PH Edelman in 1980 …

While the study of planar lattices goes back to the 1970s (KA Baker, PC Fishburn, and FS
Roberts [20] and D. Kelly and I. Rival [223]), a systematic study of planar semimodular …

Join-distributive lattices are finite, meet-semidistributive, and semimodular lattices. They are
the same as lattices with unique irreducible decompositions, introduced by RP Dilworth in …

For finite reflection groups of types $ A $ and $ B $, we determine the diameter of the graph
whose vertices are reduced words for the longest element and whose edges are braid …

Let H→ and K→ be finite composition series of length h in a group G. The intersections of
their members form a lattice CSL (H→, K→) under set inclusion. Our main result determines …

Let L be a join-distributive lattice with length n and width (Ji L)≤ k. There are two ways to
describe L by k− 1 permutations acting on an n-element set: a combinatorial way given by …

Interval parking functions (IPFs) are a generalization of ordinary parking functions in which
each car is willing to park only in a fixed interval of spaces. Each interval parking function …

Let Q be a finite quiver without oriented cycles, and let k be an algebraically closed field. The
main result in this paper is that there is a natural bijection between the elements in the …

Using the standard Coxeter presentation for the symmetric group $ S_n $, two reduced
expressions for the same group element are said to be commutation equivalent if we can …