This memoir is a refinement of the author's PhD thesis—written at Cornell University (2006).
It is primarily a desription of new research but we have also included a substantial amount of …

Abstract In a 1972 paper, Germain Kreweras investigated noncrossing partitions under the
refinement order relation. His paper set the stage both for a wealth of further enumerative …

The theory of 2-structures provides a convenient framework for decomposition and
transformation of mathematical systems where one or several different binary relationships …

The Fine numbers and the Catalan numbers are intimately related. Two manifestations are
the identity C n= 2F n+ F n− 1, n⩾ 1, and the generating function identities F= C/(1+ zC), C …

1. INTRODUCTION. Certain mathematical structures make a habit of turning up in the most
diverse of settings. Some obvious examples exhibiting this intrusive type of behavior include …

A new bijection between ordered trees and 2-Motzkin paths is presented, together with its
numerous consequences regarding ordered trees as well as other combinatorial structures …

These lecture notes provide a comprehensive, self-contained introduction to the analysis of
Wishart matrix moments. This study may act as an introduction to some particular aspects of …

The Catalan numbers constitute one of the most important sequences in combinatorics.
Catalan objects have been generalized in various directions, including the classical Fuss …

High-dimensional linear bandits with low-dimensional structure have received considerable
attention in recent studies due to their practical significance. The most common structure in …

A partition u of [k]={1, 2,⋯, k} is contained in another partition v of [l] if [l] has ak-subset on
which v inducesu. We are interested in counting partitions v not containing a given partition …