This book gives an introduction to and an overview of the methods used in the combinatorics
of pattern avoidance and pattern enumeration in set partitions, a very active area of research …

Constructions for Cyclic Sieving Phenomena Page 1 CONSTRUCTIONS FOR CYCLIC SIEVING
PHENOMENA* ANDREW BERGET†, SEN-PENG EU‡, AND VICTOR REINER§ Abstract. We …

The Catalan numbers C k were first studied by Euler, in the context of enumerating
triangulations of polygons P k+ 2. Among the many generalizations of this sequence, the …

Both the format and guiding vision of Handbook of Linear Algebra remain unchanged, but a
substantial amount of new material has been included in the second edition. The length has …

Noncrossing set partitions, nonnesting set partitions, Dyck paths, and rooted plane trees are
four classes of Catalan objects which carry a notion of type. There exists a product formula …

In this paper we provide three results involving large Schr $\ddot {o} $ der paths. First, we
enumerate the number of large Schr $\ddot {o} $ der paths by type. Second, we prove that …