This paper presents a parallel implementation of a new permutation generation method. This permutation generation method is based on the starter sets for listing all the n! permutations. The sequential algorithm is developed and parallelized for parallel computing by integrating with Message Passing Interface (MPI) libraries. The performance of the parallel algorithms is presented to demonstrat...

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

Lauren Williams (joint work with Einar Steingrímsson) We introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the " Le-diagrams " of Alex Postnikov. The structure of these tableaux is in some ways more transparent than the structure of permutations; therefore we believe tha...

Exploiting the empirical observation that the probability of k fixed points in a Welch Costas permutation is approximately the same as in a random permutation of the same order, we propose a stochastic model for the most probable maximal number of fixed points in a Welch Costas permutation.

Let H be a subgroup of the multiplicative group of a finite field. In this note we give a method for constructing permutation polynomials over the field using a bijective map from H to a coset of H. A similar, but inequivalent, method for lifting permutation behaviour of a polynomial to an extension field is also given.

The feasible monotone interpolation method has been one of the main tools to prove the exponential lowerbounds for relatively weak propositional systems. In [2], we introduced a simple combinatorial reasoning system, GCNF+permutation, as a candidate for an automatizable, though powerful, propositional calculus. We show that the monotone interpolation method is not applicable to prove the superp...

In this paper highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on N there is another permutation β on N such that the subgroup generated by α and β is highly transitive. The Baire category method is u...

We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length n and the number of occurrences of the dashed pattern 32–1 in permutations on [n]. We introduce the inversion number of a permutation tableau. For a permutation tableau T and the permutation π obtained from T by the bijection of Corteel and Nadeau, we show that the inversion number of T equals ...

Let W (π) be either the number of descents or inversions of a permutation π ∈ Sn. Stein’s method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the first use of Stein’s method in theory of permutation statistics. The construction of an exchangeable pair (W,W ) used in Stein’s method is non-trivial and may be of in...