We show the existence of a unital subalgebra β n of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that β n is… Expand

We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a… Expand

It is proved that the order complex of a geometric lattice has a convex ear decomposition and a combinatorial flag h-vector proof of hi-1 ≤ hi when i ≤ (2/7)(r + (5/2)).Expand

The peak set of a permutation σ is the set {i : σ(i − 1) < σ(i) > σ(i + 1)}. The group algebra of the symmetric group Sn admits a subalgebra in which elements are sums of permutations with a common… Expand

Permutation modules are fundamental in the representation theory of symmetric groups $\Sym_n$ and their corresponding Iwahori--Hecke algebras $\He = \He(\Sym_n)$. We find an explicit combinatorial… Expand

A more comprehensive list of classes of bitolerance orders is provided and equality between some of these classes in general and other classes in the bipartite domain is proved.Expand

A collection of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices are given.Expand

The peak algebra $$\mathfrak{P}_{n}$$ is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of… Expand