Sunder and Wildberger (J. Algebr. Comb. 18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *action, then K arises from an association scheme. In this paper we will fi...

Finding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n+k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k max...

We prove a strong form of the Brumer–Stark Conjecture and, as a consequence, a strong form of Rubin’s integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k contained in the compositum kp∞ := kp · k∞ of the maximal pro-p abelian extension kp/k and the maximal...

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i.e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)

A collection of edge-disjoint triangle-factors on K3n is called maximal if it cannot be extended by a further triangle-factor. It is well-known that a maximal set must therefore contain at least % triangle factors. We consider the following question: for which k with % :::; k :::; (3n;1) is there a maximal set of k trianglefactors on K3n?

Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A . If B= A , it is shown that the following conditions are equivalent: (i) B i...

Fix integers n and k with n ≥ k ≥ 3. Duffus and Sands proved that if P is a finite poset and n ≤ |C| ≤ n+ (n− k)/(k− 2) for every maximal chain in P , then P must contain k pairwise disjoint maximal antichains. They also constructed a family of examples to show that these inequalities are tight. These examples are 2-dimensional which suggests that the dual statement may also hold. In this paper...

Let k and b be integers with k > 1. A set A of integers is called (k, b)linear-free if x E A implies kx + b ¢ A. Such a set A is maximal in [I,n] = {1,2, ... ,n} if AU{t} is not (k,b)-linear-free for any t in [1,nJ\A. Let M = M(n, k, b) be the set of all maximal (k, b)-linear-free subsets of [1, n] and define f(n, k, b) = max{IAI : A E M} and g(n, k, b) = min{IAI : A EM}. In this paper a new me...

Optical orthogonal codes (OOCs) are used in optical code division multiple access systems to allow a large number of users communicate simultaneously with low error probability. The simultaneous is at most as big the codewords such code. We consider (v,k,2,1)-OOCs, namely OOCs length v, weight k, auto-correlation 2, and cross-correlation 1. An upper bound B0(v,k,2,1) on maximal an OOC was deriv...

A graph G has maximal local edge-connectivity k if the maximum number of edge-disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks-type theorems for k-connected graphs with maximal local edge-connectivity k, and for any graph with maximal local edge-connectivity 3. We also consider several related graph classes defined by constraints on connectivity. In p...