Given the set [n] = {1, . . . , n} for positive integer n, combinatorial properties of Clifford algebras are exploited to count partitions and non-overlapping partitions of [n]. The result is… (More)

While powers of the adjacency matrix of a finite graph reveal information about walks on the graph, they fail to distinguish closed walks from cycles. Using elements of an appropriate commutative,… (More)

A number of combinatorial problems are treated using properties of abelian nilpotentand idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a… (More)

Questions about a graph’s connected components are answered by studying appropriate powers of a special “adjacency matrix” constructed with entries in a commutative algebra whose generators are… (More)

Classical approaches to multi-constrained routing problems generally require construction of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the notion of… (More)

Nilpotent and idempotent adjacency operator methods are applied to the study of random geometric graphs in a discretized, d-dimensional unit cube [0, 1]. Cycles are enumerated, sizes of maximal… (More)

Central to the theory of free probability is the notion of summing multiplicative functionals on the lattice of non-crossing partitions. In this paper, a graph-theoretic perspective of partitions is… (More)

Appell systems can be interpreted as polynomial solutions of generalized heat equations, and in probability theory they have been used to obtain non-central limit theorems. The natural… (More)

Wireless sensor networks (WSN) are inherently multi - constrained. They need to preserve energy while offering reliable and timely data reporting for a non-negligible number of scenarios. This is… (More)