The Halton sequence is one of the classical low-discrepancy sequences. It is effectively used in numerical integration when the dimension is small, however, for larger dimensions, the uniformity of the sequence quickly degrades. As a remedy, generalized (scrambled) Halton sequences have been introduced by several researchers since the 1970s. In a generalized Halton sequence, the digits of the o...

We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations of class-preserving automorphisms and permutation representations with the same character in terms of Drinfel'd algebras are also given.

This paper shows how the Kazhdan-Lusztig theory of cells can be directly applied to establish the quasi-heredity of q-Schur algebras. The application arises because of a very strong homological property enjoyed by certain cell filtrations for q-permutation modules.

Abstract Using algebraic techniques, one of the co-authors has designed a [155,64,20] low density parity check code based on permutation matrices. This code is quasi-cyclic by construction and hence admits a convolutional representation. A set of low density parity check convolutional codes is derived from this quasi-cyclic code and its generalizations. We investigate the performance of these c...

For any class C of bipartite graphs, we define quasi-C to be the class of all graphs G such that every bipartition of G belongs to C. This definition is motivated by a generalisation of the switch Markov chain on perfect matchings from bipartite graphs to nonbipartite graphs. The monotone graphs, also known as bipartite permutation graphs and proper interval bigraphs, are such a class of bipart...

We prove that if the squares of two unconditional bases are equivalent up to a permutation, then themselves permutatively equivalent. This settles twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides new paradigm study uniqueness basis general framework quasi-Banach spaces. Multiple examples given illustrate how put practice theoretical scheme. Among...

In this paper we introduce the concept of the quasi-product of tree automata. In a quasi-product the inputs of the component tree automata are operational symbols in which permutation and unification of variables are allowed. It is shown that in sets of tree automata which are homomorphically complete with respect to the quasiproduct the essentially unary operations play the basic role among al...

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

In [2], we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper, we show that for a finite p-group G, where p is a prime, q(G) = p(G). Moreover, for odd prime p, c(G) = q(G) = p(G). 2000 Mathematics Subject Classification: primary 20D15; secondary 20B05, 20C15