The VMPC function is a combination of triple permutation composition and integer addition. It differs from a simple triple permutation composition with one integer addition operation performed on some of the elements of the permutation. The consequence of this addition operation is corruption of cycle structure of the transformed permutation the fundamental source of the function's resistance t...

Any permutation polynomial is an n -cycle permutation. When a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These have important applications in cryptography coding theory. Inspired by the AGW Criterion, we propose criteria for which mainly are of form x r h ( s ) . We then unified constru...

The VMPC function is a combination of triple permutation composition and integer addition. It differs from a simple triple permutation composition with one integer addition operation performed on some of the elements of the permutation. The consequence of this addition operation is corruption of cycle structure of the transformed permutation the fundamental source of the function's resistance t...

Recently the operator algebra, including the twisted affine primary fields, and a set of twisted KZ equations were given for the WZW permutation orbifolds. In the first part of this paper we extend this operator algebra to include the so-called orbifold Virasoro algebra of each WZW permutation orbifold. These algebras generalize the orbifold Virasoro algebras (twisted Virasoro operators) found ...

In-situ permutation algorithms are algorithms to permute an array of n items without using a second array. Few space is needed when one proceeds permuting along a cycle. Thus, those algorithms first search for one element called leader on each cycle of the permutation. Then they move the items cycle by cycle. A great fraction of the runtime is spent with testing whether elements are leaders. We...

In this paper, we establish a natural bijection between the almost-increasing cyclic permutations of length n and unimodal permutations of length n − 1. This map is used to give a new characterization, in terms of pattern avoidance, of almostincreasing cycles. Additionally, we use this bijection to enumerate several statistics on almost-increasing cycles. Such statistics include descents, inver...

The space of permutation pseudographs is a probabilistic model of 2-regular pseudographs on n vertices, where a pseudograph is produced by choosing a permutation σ of {1, 2, . . . , n} uniformly at random and taking the n edges {i, σ(i)}. We prove several contiguity results involving permutation pseudographs (contiguity is a kind of asymptotic equivalence of sequences of probability spaces). Na...