We study novel approaches for solving of hard combinatorial problems by translation to Boolean Satisfiability (SAT). Our focus is on combinatorial problems that can be represented as a permutation of n objects, subject to additional constraints. In the case of the Hamiltonian Cycle Problem (HCP), these constraints are that two adjacent nodes in a permutation should also be neighbors in the grap...

We describe the close relationship between permutation groups and combinatorial species (introduced by A. Joyal, Adv. in Math. 42, 1981, l-82). There is a bijection @ between the set of transitive actions (up to isomorphism) of S, on finite sets and the set of “molecular” species of degree n (up to isomorphism). This bijection extends to a ring isomorphism between B(S,) (the Burnside ring of th...

In this work we introduce and study a set of new interleavers based on permutation polynomials and functions with known inverses over a finite field Fq for using in turbo code structures. We use Monomial, Dickson, Möbius and Rédei functions in order to get new interleavers. In addition we employ Skolem sequences in order to find new interleavers with known cycle structure. As a byproduct we giv...

We report on our experiences with the implementation of a parallel algorithm to compute the cycle structure of a permutation given as an oracle. As a sub-problem, the cycle structure of a modified permutation given as a table that is partitioned over N hard disks has to be computed. While a minor point during algorithm design and analysis, we spent most time to implement and tune this particula...

We study permutations of the set [n] = {1, 2, . . . , n} written in cycle notation, for which each cycle forms an increasing or decreasing interval of positive integers. More generally, permutations whose cycle elements form arithmetic progressions are considered. We also investigate the class of generalised interval permutations, where each cycle can be rearranged in increasing order to form a...

The set of permutations generated by cyclic shift is studied using a number system coding for these permutations. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code describing structural and symmetry properties of the set of permutations ordered according to generation by cyclic shift. The code is...

We consider the enumeration of unlabeled directed hypergraphs by using Pólya’s counting theory and Burnside’s counting lemma. Instead of characterizing the cycle index of the permutation group acting on the hyperarc set A, we treat each cycle in the disjoint cycle decomposition of a permutation ρ acting on A as an equivalence class (or orbit) of A under the operation of the group generated by ρ...

In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field Fq. For the first time Möbius and Rédei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Rédei functions an exact formula for ...