Let S be a subset of the positive integers, and let σ be a permutation of S. We say that σ is a k-avoiding permutation of S if σ does not contain any k-term AP as a subsequence. Similarly, the set S is said to be k-avoidable if there exists a k-avoiding permutation of S.

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

To every involutive non-degenerate set-theoretic solution [Formula: see text] of the Yang–Baxter equation on a finite set there is naturally associated solvable permutation group acting text]. We prove that primitive this type prime order Moreover, then so-called determined by cycle length This solves problem recently asked A. Ballester-Bolinches. The result opens new perspective possible appro...

A graph dynamical system consists of an undirected graph Y where each vertex is assigned a state from a finite set K, an update function for each vertex that depends only on the state of the vertex and its neighbors, and a method that dictates how to compose these functions. A common subclass of graph dynamical systems are sequential dynamical systems, or SDSs, where the update functions are ap...

the group $2^6{{}^{cdot}} g_2(2)$ is a maximal subgroup of the rudvalis group $ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. in this paper, we construct the character table of the group $2^6{{}^{cdot}} g_2(2)$ by using the technique of fischer-clifford matrices.

Golomb and Gaal [15] study the number of permutations on n objects with largest cycle length equal to k. They give explicit expressions on ranges n/(i + 1) < k ≤ n/ i for i = 1, 2, . . . , derive a general recurrence for the number of permutations of size n with largest cycle length equal to k, and provide the contribution of the ranges (n/(i + 1), n/ i] for i = 1, 2, . . . , to the expected le...

Evolutionary algorithms solve problems by simulating the evolution of a population candidate solutions. We focus on evolving permutations for ordering such as traveling salesperson problem (TSP), well assignment quadratic (QAP) and largest common subgraph (LCS). propose cycle mutation, new mutation operator whose inspiration is well-known crossover operator, concept permutation cycle. use fitne...