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...

Semantics extensions are the outcome of the argumentation reasoning process: enumerating them is generally an intractable problem. For preferred semantics two efficient algorithms have been recently proposed, PrefSAT and SCC-P, with significant runtime variations. This preliminary work aims at investigating the reasons (argumentation framework features) for such variations. Remarkably, we obser...

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...

In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind problems arises whenever associated decision-makers have their respective many solutions. For purpose, we develop branch-and-cut algorithm based on programming, for finding solutions in terms both and ...

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...