In a 1937 paper B. H. Neumann constructed an uncountable family of 2-generated groups. We prove that all his groups are permutation stable by analyzing the structure their invariant random subgroups.

The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. A...

Software watermarking has received considerable attention and was adopted by the software development community as a technique to prevent or discourage software piracy and copyright infringement. A wide range of software watermarking techniques has been proposed among which the graph-based methods that encode watermarks as graph structures. Following up on our recently proposed methods for enco...

BACKGROUND Advanced intercross lines (AIL) are segregating populations created using a multi-generation breeding protocol for fine mapping complex trait loci (QTL) in mice and other organisms. Applying QTL mapping methods for intercross and backcross populations, often followed by naïve permutation of individuals and phenotypes, does not account for the effect of AIL family structure in which f...

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...

We study the metacommutation problem in Eichler orders. From this arises a permutation of set locally principal left ideals given prime reduced norm. Previous results on cycle structure were determined for maximal As we ext

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.

Motivated by the proof of Rump a conjecture Gateva-Ivanova on decomposability square-free solutions to Yang-Baxter equation, we present several other theorems based cycle structure certain permutation associated with solution.