The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1, 2, . . . , n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1 . . . n] be an array of n integer keys each in th...

We extend the work which has appeared in papers on sharp characters and originated with Blichfeldt and Maillet to the Burnside ring of a finite group G. We show that the polynomial whose zeros are the set of marks of non-identity subgroups on a faithful G-set X evaluated at X is an integral multiple of the regular G-set, and deduce a result about the size of a base of X . Further consequences f...

Contemporary real-time problems like CAPTCHA generation and optical character recognition can be solved effectively using correlated random fields. These random fields should be produced on a graph in order that problems of any dimension and shape can be handled. However, traditional solutions are often too slow, inaccurate or both. Herein, the Quick Simulation Random Field algorithm to produce...

It is well known that if a finite graded lattice of rank n is supersolvable, then it has an EL-labeling where the labels along any maximal chain form a permutation. We call such a labeling an Sn EL-labeling and we show that a finite graded lattice of rank n is supersolvable if and only if it has such a labeling. We next consider finite graded posets of rank n with 0̂ and 1̂ that have an Sn EL-lab...

We introduce the class of permutation bigraphs as an analogue of permutation graphs. We show that this is precisely the class of bigraphs having Ferrers dimension at most 2. We also characterize the subclasses of interval bigraphs and indifference bigraphs in terms of their permutation labelings, and we relate permutation bigraphs to posets of dimension 2.

Two completely new algorithms for generating permutations–shift cursor algorithm and level algorithm–and their efficient implementations are presented in this paper. One implementation of shift cursor algorithm gives an optimal solution of permutation generation problem, and one implementation of level algorithm can be used to generate random permutations.

We give a recursive formula for the Möbius function of an interval [σ, π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1, 2, . . . , k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficie...

We consider the problem of enumerating polynomials over Fq, that have certain coefficients prescribed to given values and permute certain substructures of Fq. In particular, we are interested in the group of N -th roots of unity and in the submodules of Fq. We employ the techniques of Konyagin and Pappalardi to obtain results that are similar to their results in [Finite Fields and their Applica...

P ∈ SN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is (N) if one does not us...