A graph model based on single character operations is developed for constructing the median of two strings X and Y. Vertices represent stages of median construction and edges correspond to processing one or both characters of the two strings. In this paper, the median is defined as a string having the median character frequency of each character over the two strings and which minimizes the maxi...

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

We determine the finite simple groups of Lie type of characteristic p, for which the Steinberg character lies in the principal `-block for every prime ` 6= p dividing the order of the group. In [1, Corollary 4.4], Bessenrodt, Malle, and Olsson determine the finite simple groups of Lie type having a non-trivial irreducible character which is in the principal `-block for all primes ` dividing the...

We investigate the problem of detecting periodic trends within a string S of length n, arriving in the streaming model, containing at most k wildcard characters, where k = o(n). A wildcard character is a special character that can be assigned any other character. We say S has wildcard-period p if there exists an assignment to each of the wildcard characters so that in the resulting stream the l...

Character sums over finite fields have been widely studied since Gauss. During the last decade, coding theorists initiated the study of a new type of sums, over points with coordinates in a p-adic field. Let O (u) m be the ring of integers of Q p(ζpm−1), the unramified extension of degree m of the field of p-adic numbers Q p obtained by adjoining the (p−1)-th roots of unity, Tm = T ∗ m∪{0}, whe...