A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel
Research Directions Focusing on a very active area of research in the last decade …

This book is about how symmetric functions can be used in enumeration. The development
is entirely self-contained, including an extensive introduction to the ring of symmetric …

We consider the graph G n with vertex set V (G n)={1, 2,…, n} and {i, j}∈ E (G n) if and only if
0<| i− j|≤ 2. We call G n the straight linear 2-tree on n vertices. Using Δ–Y transformations …

Providing a self-contained resource for upper undergraduate courses in combinatorics, this
text emphasizes computation, problem solving, and proof technique. In particular, the book …

Let s and t be variables. Define polynomials {n} in s, t by {0}= 0,{1}= 1, and {n}= s {n–1}+ t {n–
2} for n≥ 2. If s, t are integers then the corresponding sequence of integers is called a Lucas …

We introduce the notion of a Mahonian pair. Consider the set, P⁎, of all words having the
positive integers as alphabet. Given finite subsets S, T⊂ P⁎, we say that (S, T) is a …

Given two variables s and t, the associated sequence of Lucas polynomials is defined
inductively by {0}= 0,{1}= 1, and {n}= s {n− 1}+ t {n− 2} for n≥ 2. An integer (eg, a Catalan …

We study three operations on Riordan arrays. First, we investigate when the sum of Riordan
arrays yields another Riordan array. We characterize the $ A $-and $ Z $-sequences of …

We consider the set partition statistics ls and rb introduced by Wachs and White and
investigate their distribution over set partitions that avoid certain patterns. In particular, we …

We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci
identities. As a special case, we propose an elliptic extension which extends the q-Fibonacci …