There has been considerable interest recently in the subject of patterns in permutations and
words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and …

An endhered (end-adhered) pattern is a subset of arcs in matchings, such that the
corresponding starting points are consecutive, and the same holds for the ending points …

Extending the notion of pattern avoidance in permutations, we study matchings and set
partitions whose arc diagram representation avoids a given configuration of three arcs …

We give a correspondence between graphs with a given degree sequence and fillings of
Ferrers diagrams by nonnegative integers with prescribed row and column sums. In this …

An ordered matching of size $ n $ is a graph on a linearly ordered vertex set $ V $, $| V|= 2n
$, consisting of $ n $ pairwise disjoint edges. There are three different ordered matchings of …

We develop a combinatorial model of the associated Hermite polynomials and their
moments, and prove their orthogonality with a sign-reversing involution. We find …

A matching of the set [2 n]={1, 2,…, 2 n} is a partition of [2 n] into blocks with two elements, ie
a graph on [2 n], such that every vertex has degree one. Given two matchings σ and τ, we …

Borel's triangle is an array of integers closely related to the classical Catalan numbers. In
this paper we study combinatorial statistics counted by Borel's triangle. We present various …

Let M,N be two matchings on 2n (possibly M=N). For an integer l≥0, let \calT(M,l) be the set
of those matchings on 2n+2l which can be obtained from M by successively adding l times …

In this thesis we obtained combinatorial proofs in three different areas. Since the three topics
are separated problems in enumerative combinatorics, we found it necessary to make the …