Let ai,j(n) denote the number of walks in n steps from (0, 0) to (i, j), with steps (±1, 0) and (0,±1), never touching a point (−k, 0) with k ≥ 0 after the starting point. Bousquet-Mélou and Schaeffer conjectured a closed form for the number a −i,i(2n) when i ≥ 1. In this paper, we prove their conjecture, and give a formula for a −i,i(2n) for i ≤ −1.

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 investigate a Genetic Algorithm (GA) solution for the NP-hard Leaf Constrained Minimal Spanning Tree (LCMST) problem on a weighted complete graph using a novel encoding for the genotype which ensures feasibility of the search space when performing crossover and mutation and when initializing the population. The feasible genotype for the LCMST problem is a permutation code (an adaptation of t...

In this paper, we develop a constant amortized time (CAT) algorithm for generating permutations with a fixed number of excedances. We obtain a Gray code for permutations having one excedance. We also give a bijection between the set of n-length permutations with exactly one excedance and the set Sn(321, 2413, 3412, 21534)\{123 . . . (n− 1)n}. This induces a Gray code for the set Sn(321, 2413, 3...

A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ω-categorical structures, i.e., countably infinite structures with a firstorder theory that has only one countab...

In 2000 Klazar introduced a new notion of pattern avoidance in the context of set partitions of [n] = {1, . . . , n}. The purpose of the present paper is to undertake a study of the concept of Wilf-equivalence based on Klazar’s notion. We determine all Wilf-equivalences for partitions with exactly two blocks, one of which is a singleton block, and we conjecture that, for n ≥ 4, these are all th...

During compilation of a program, register allocation is the task of mapping program variables to machine registers. During register allocation, the compiler may introduce shuffle code, consisting of copy and swap operations, that transfers data between the registers. Three common sources of shuffle code are conflicting register mappings at joins in the control flow of the program, e.g, due to i...

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...

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to a trivial normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained from codes as above. With every IBIS group is associated a matroid; in the case of a group from a code, the matroid differs only trivially from that which arise...

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained from codes as above. With every IBIS group is associated a matroid; in the case of a code group, the matroid differs only trivially from that which arises from the code. ...