Finding a sequence of transpositions that transforms a given permutation into the identity permutation and is of the shortest possible length is an important problem in bioinformatics. Here, a transposition consists in exchanging two contiguous intervals of the permutation. Bafna and Pevzner introduced the cycle graph as a tool for working on this problem. In particular, they took advantage of ...

The cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles:

A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in as few moves as possible, using a given set of allowed operations, or computing the number of moves the sorting process requires, often referred to as the distance of the permutation. These operations often act on just one or tw...

we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...

This is not the only way to write (abc) using transpositions, e.g., (abc) = (bc)(ac) = (ac)(ab). Since any permutation in Sn is a product of cycles and any cycle is a product of transpositions, any permutation in Sn is a product of transpositions. 1 Unlike the unique decomposition of a permutation into a product of disjoint cycles, the decomposition of a permutation as a product of transpositio...

We study the permutations of the finite field Fqn given by x + γ f(x), where γ ∈ Fqn is a linear translator of f : Fqn → Fq. We determine the cycle structure and the inverse of such a permutation. We describe several families of permutation polynomials obtained using functions with linear translators.

2011 Using the reciprocal to calculate generating functions for permutations with no consecutive pattern matches Permutation Patterns 2011 San Luis Obispo, CA 2011 Reciprocal method to enumerate permutations with no consecutive pattern matches FPSAC 2011 Reykjavik, Iceland 2010 Pattern matching in the cycle structure of permutations Permutation Patterns 2010 Dartmouth, NH 2010 Advancement to ca...

Discrete functional limit theorems, which give independent process approximations for the joint distribution of the component structure of combinatorial objects such as permutations and mappings, have recently become available. In this article, we demonstrate the power of these theorems to provide elementary proofs of a variety of new and old limit theorems, including results previously proved ...