Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one
possible generalization of the Catalan numbers. We will present a new combinatorial object …

We present a simple greedy algorithm for generating Gray codes for Dyck words and fixed-
weight Dyck prefixes. Successive strings in our listings differ from each other by a …

Ordered trees are called non-regular trees with a prescribed branching sequence (or non-
regular trees for short) if their internal nodes have a pre-specified degree sequence in …

In this paper, we present two new ranking and unranking algorithms for z-sequences in Gray-
code order. These algorithms are designed based on a loopless generation algorithm which …

For any given k, the sequence of k-ary Catalan numbers, Ct, k= 1kt+ 1 (ktt), enumerates a
number of combinatorial objects, including k-ary Dyck words of length n= kt and k-ary trees …

In this paper, we introduce a concise representation, called right-distance sequences (or RD-
sequences for short), to describe all t-ary trees with n internal nodes. A result reveals that …

We present a simple algorithm that generates a cyclic 2-Gray code for ballot sequences. The
algorithm generates each ballot sequence in constant amortized time using a linear amount …

A t-ary tree is a rooted tree such that every internal node has exactly t disjoint subtrees.
Recently, a concise representation called right-distance sequences (RD-sequences) was …

A non-regular tree T with a prescribed branching sequence (s 1, s 2,..., sn) is a rooted and
ordered tree such that its internal nodes are numbered from 1 to n in preorder and every …

The aim in this paper is to collect in one place a list of currently known and new structures
enumerated by the k-ary numbers. Some of the structures listed already exist in the folk-lore …