The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [...
William Y. C. Chen, Susan Y. J. Wu, Catherine H. Y...
The motivation for this paper is three-fold. First, we study the connectivity properties of the homomorphism order of directed graphs, and more generally for relational structures...
Wang and Lih conjectured that for every g 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree M(g) is (+1)-colorable. ...
Given the set [n] = {1, . . . , n} for positive integer n, combinatorial properties of Clifford algebras are exploited to count partitions and nonoverlapping partitions of [n]. Th...
We present a combinatorial proof of Postnikov's hook length formula for binary trees. c 2007 Elsevier Ltd. All rights reserved. Let [n] = {1, 2, . . . , n}. It is well known ...
Let D be a set of positive integers. The distance graph generated by D, denoted by G(Z, D), has the set Z of all integers as the vertex Supported in part by the National Science ...
A linear deformation of a Meyer set M in Rd is the image of M under a group homomorphism of the group [M] generated by M into Rd . We provide a necessary and sufficient condition f...
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n-...
Catherine S. Greenhill, Fred B. Holt, Nicholas C. ...