On an enumeration problem

A Noncommutative Enumeration Problem

An Improved Enumeration Scheme for Subset Sum Problem

The subset sum problem (SSP) can be briefly stated as: given a target integer E and a set A containing n positive integer aj , find a subset of A summing to E. The density d of an SSP instance is defined by the ratio of n to m, where m is the logarithm of the largest integer within A. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme fo...

Enumeration Algorithm for the Edge Coloring Problem on Bipartite Graphs

In this paper, we propose an algorithm for nding all the edge colorings in bipartite graphs. Our algorithm requires O(T (n;m; ) + Kminfn 2 +m; T (n;m; )g) time and O(m ) space, where n denotes the number of vertices, m denotes the number of edges, denotes the number of maximum degree, T (n;m; ) denotes the time complexity of an edge coloring algorithm, and K denotes the number of edge colorings.

An Enumeration Algorithm for the Edge Coloring Problem on Bipartite Graphs

In this paper, we propose an algorithm for nding all the edge colorings in bipartite graphs. Our algorithm requires O(m log + Kminfn 2 +m;m log g) time and O(m ) space, where n denotes the number of vertices, m denotes the number of edges, denotes the number of maximum degree, and K denotes the number of edge colorings.

On an open problem of Green and Losonczy: exact enumeration of freely braided permutations

Recently, Green and Losonczy [5, 6] introduced freely braided permutations as a special class of restricted permutations that has arisen in the study of Schubert varieties. They suggest as an open problem to enumerate the number of freely braided permutations in Sn. In this paper, we prove that the generating function for the number of freely braided permutations in Sn is given by 1−3x−2x2 +(1+...