We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon, and demonstrate that these are closely related to the pattern...

In this paper, we used the permutation group together with concept of cordiality in graph theory to introduce a new method labeling. This construed permuted cordial labeling can be applied all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated show that union any two paths cycles addition, for path cycle.

Let k ≥ 2 be an integer and T1, . . . , Tk be spanning trees of a graph G.If for any pair of vertices (u, v) of V (G), the paths from u to v in each Ti,1 ≤ i ≤ k, do not contain common edges and common vertices, except thevertices u and v, then T1, . . . , Tk are completely independent spanningtrees in G. For 2k-regular graphs which are 2k-connected, such as theCartesian pro...

Abstract In this study, first, the definitions of preference relation matrix and 0-1 permutation linguistic judgement are given. The method judging satisfactory consistency by standard arrangement is obtained. This not only solves problem when there no equivalent objects but also simple effective. Then, definition cyclic circle three According to size value object line, cycle adjusted language ...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 22 April 2021Accepted: 14 September 2021Published online: 30 November 2021KeywordsEulerian polynomials, bijection, permutation statistic, equidistribution, cycle, continued fraction, descent, excedance, drop, derangement, gamma-positivityAMS Subject Headings05A05, 05A15, ...

As data about genomic architecture accumulates, genomic rearrangements have attracted increasing attention. One of the main rearrangement mechanisms, inversions (also called reversals), was characterized by Hannenhalli and Pevzner and this characterization in turn extended by various authors. The characterization relies on the concepts of breakpoints, cycles, and obstructions colorfully named h...

In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a of elements full monomial group exploit this describe conjugacy classes centralisers group. We generalise their results wreath products whose base need not be finite top acts faithfully on set. parameterise such explicitly. For products, our approach yields efficient algorithms for finding conjugating ...

We study the problem of sorting by transpositions, which consists in computing the minimum number of transpositions required to sort a permutation. This problem is NP-hard and the best approximation algorithms for solving it are based on a standard tool for attacking problems of this kind, the cycle graph. In an attempt to bypass it, some researches posed alternative approaches. In this paper, ...

We describe an efficient construction of pseudorandom permutations P with the fast forward property, namely, such that for each m the computation of Pm(x) can be done with a constant number of calls to an underlying pseudorandom permutation. This solves an open problem of Naor and Reingold. 1. Ordered cycle structures Definition 1.1. Let Ω be a finite, well-ordered set. The ordered cycle struct...