R\I stands for the set of positive integers, and li$, for the set of non-negative integers. If S is a set then IS( is the number of elements of S. If S is a set, then a multiset of elements of S is a mapping f of S into &, with the property that the set of s with f(s)>0 is finite. The set of all these multisets is denoted M(S). Some of our multisets are multisets of natural numbers. Number theo...

We consider a new way of looking at multisets, involving linear rather than multiplicative notation and operations which mirror those on natural numbers. The motivation is to create a framework for mathematics which more closely connects with scientific usage in which repetition and relative concepts of equality play an important role. The tropical calculus is introduced as an important tool. a...

Short, bijective proofs of identities for multisets of ‘hook pairs’ (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.

We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.

Short, bijective proofs of identities for multisets of ‘hook pairs’ (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.

The notion of a q-representative set for a family of subsets has recently proven to be very useful in the design of parameterized and exact algorithms. We generalize this notion to families of multisets. We also give an efficient way to find a representative set for a family of multisets. As an application we give a deterministic algorithm for minimal weight r-SIMPLE k-PATH running in time O(r)...

Recently three approaches for solving planning problems deductively were proposed each of which does not require to state frame axioms explicitly. These approaches are based on the linear connection method, an equational logic programming language, and on linear logic. In this paper, we briefly review these approaches and show that they are equivalent. Moreover, we illustrate that these approac...