Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce notion permutation resemblance a function, which looks to measure distance given map is from being permutation. We prove several results concerning permutation resemblance and show how it can ...

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type ...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

Let C be a conjugation class of permutations of a finite field Fq. We consider the function NCðqÞ defined as the number of permutations in C for which the associated permutation polynomial has degree 5q 2. In 1969, Wells proved a formula for N1⁄23 ðqÞ where 1⁄2k denotes the conjugation class of k-cycles. We will prove formulas for N1⁄2k ðqÞ where k 1⁄4 4; 5; 6 and for the classes of permutation...