Let k and m be positive integers. A collection of k-multisets from {1, . . . ,m} is intersecting if every pair of multisets from the collection is intersecting. We prove that for m ≥ k +1, the size of the largest such collection is ( m+k−2 k−1 ) and that when m > k + 1, only a collection of all the k-multisets containing a fixed element will attain this bound. The size and structure of the larg...

Gamma is a programming model where computation can be seen as chemical reactions between data represented as molecules floating in a chemical solution. This model can be formalized as associative, commutative, conditional rewritings of multisets where rewrite rules and multisets represent chemical reactions and solutions, respectively. In this article, we generalize the notion of multiset used ...

In this paper, we use submajorization to compare distances between either multisets of real numbers or multisets modulo translation on the real line. We provide a geometrical interpretation in which multisets are represented by points in an orbifold and bijections between multisets are represented by paths between these points. This interpretation shows that submajorization is closely related t...

This paper contains analysis of creation of sets and multisets as an approach for modeling of some aspects of human thinking. The creation of sets is considered within constructive object-oriented version of set theory (COOST), from different sides, in particular classical set theory, object-oriented programming (OOP) and development of intelligent information systems (IIS). The main feature of...

We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below 0. In Isabelle/HOL, both nested and hereditar...

Gamma is a programming model where computation can be seen as chemical reactions between data represented as molecules floating in a chemical solution. This model can be formalized as associative, commutative, conditional rewritings of multisets where rewrite rules and multisets represent chemical reactions and solutions, respectively. In this article, we generalize the notion of multiset used ...

The eeect of using randomly selected sequence multisets for the uplink of a synchronous code-division multiple-access channel is considered. A tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given. For large systems, the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as th...

The effect of using randomly selected sequence multisets for the uplink of a synchronous code-division multipleaccess channel is considered. A tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given. For large systems, the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as th...

Sets and multisets are fundamental data structures which are used in numerous distributed algorithms. We investigate randomized versions of sets and multisets and show that our probabilistic approach can improve the performance of systems using our distributed shared data structures. We give algorithms for basic set and multiset operations and prove a number of fundamental properties. We illust...