We present an infinite family of recursive formulas that count binary integer partitions satisfying natural divisibility conditions and show these counts are interrelated via partial sums. Moreover, we interpret the study in language graded polynomial rings apply this to mod <mml:se...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.

Let A be a finite alphabet and let DcA * be a finite set of words to be labelled "dirty". Let {Xa: a E A} be commuting indeterminates. To every letter a E A we assign the weight Xa and the weight of a word is the product of the weights of its letters. For example, weight (13221) = X1X3X2X2X1 = XiX~X3. Given any set S of words we let weight (S) be the sum of the weights of the members of S. For ...

Let G be a simple, connected graph with finite vertex set V and edge set E . A depletion of G is a permutation v1v2v3 . . . vn of the elements of V with the property that vi is adjacent to some member of {v1, v2, · · · , vi°1} for each i ∏ 2. Depletions model the spread of a rumor or a disease through a population and are related to heaps. In this paper we develop techniques for enumerating the...

we prove that rs-bl-algebras are mv-algebras.

A dynamic programming method for enumerating hamiltonian cycles in arbitrary graphs is presented. The method is applied to grid graphs, king’s graphs, triangular grids, and three-dimensional grid graphs, and results are obtained for larger cases than previously published. The approach can easily be modified to enumerate hamiltonian paths and other similar structures.

A cycle is a sequence taken in a circular order—that is, follows , and are all the same cycle as . Given natural numbers and , a cycle of letters is called a complete cycle [1, 2], or De Bruijn sequence, if subsequences consist of all possible ordered sequences over the alphabet . In 1946, De Bruijn proved [1] (see [2]) that the number of complete cycles, under , is equal to . We propose the ov...

We introduce the concept of a segment of a degenerate convex polytope specified by a system of linear constraints, and explain its importance in developing algorithms for enumerating the faces. Using segments, we describe an algorithm that enumerates all the faces, in time polynomial in their number. The role of segments in the unsolved problem of enumerating the extreme points of a convex poly...