The study of patterns in permutations in a very active area of current research. Klazar
defined and studied an analogous notion of pattern for set partitions. We continue this work …

In this paper, we study Forman's discrete Morse theory in the context of weighted homology.
We develop weighted versions of classical theorems in discrete Morse theory. A key …

This is a brief survey of some open problems on permutation patterns, with an emphasis on
subjects not covered in the recent book by Kitaev, Patterns in Permutations and words. I first …

Klazar defined and studied a notion of pattern avoidance for set partitions, which is an
analogue of pattern avoidance for permutations. Sagan considered partitions which avoid a …

We give a recursive formula for the Möbius function of an interval [σ, π] in the poset of
permutations ordered by pattern containment in the case where π is a decomposable …

A permutation\tau contains another permutation\sigma as a pattern if\tau has a subsequence
whose elements are in the same order with respect to size as the elements in\sigma. This …

The set of all permutations, ordered by pattern containment, forms a poset. This paper
presents the first explicit major results on the topology of intervals in this poset. We show that …

The set of all permutations, ordered by pattern containment, is a poset. We give a formula for
the M\" obius function of intervals $[1,\pi] $ in this poset, for any permutation $\pi $ with at …

We present a two term formula for the Möbius function of intervals in the poset of all
permutations, ordered by pattern containment. The first term in this formula is the number of …

We prove the existence of signed combinatorial interpretations for several large families of
structure constants. These families include standard bases of symmetric and quasisymmetric …