A permutation is (1-23-4)-avoiding if it contains no four entries, increasing left to right, with the middle two adjacent in the permutation. Here we give a 2-variable recurrence for the number of such permutations, improving on the previously known 4-variable recurrence. At the heart of the proof is a bijection from (1-23-4)-avoiding permutations to increasing ordered trees whose leaves, taken...

The standard genetic code multiplet structure as well as the correct degeneracies, class by class, are all extracted from the (unique) number 23!, the order of the permutation group of 23 objects.

Article history: Received 23 January 2010 Received in revised form 23 April 2010 Accepted 26 April 2010 Available online 26 April 2010 During the past two decades, there have been increasing interests on permutation flow shop with different types of objective functions such as minimizing the makespan, the weighted mean flow-time etc. The permutation flow shop is formulated as a mixed integer pr...

1. Introduction. Let p be a prime number such that q — l{p — l) is also a prime. Let Q, be the set of symbols 1, • • • , p, and ® be a non-solvable transitive permutation group on 12. Such permutation groups were first considered by Galois in 1832 [I, §327; III, §262]: if the linear fractional group LF 2 (l) over the field of I elements, where I is a prime number not smaller than five, contains...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

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.

A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

We provide a bijection from the permutations in Sn that avoid 3412 and contain exactly one 321 pattern to the permutations in Sn+1 that avoid 321 and contain exactly one 3412 pattern. The enumeration of these classes is obtained from their classification via reduced decompositions. The results are extended to involutions in the above pattern classes using reduced decompositions reproducing a re...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...