We introduce the multiset partition algebra $${\cal M}{{\cal P}_k}\left(\xi \right)$$ over polynomial ring F[ξ], where F is a field of characteristic 0 and k positive integer. When ξ specialized to integer n, we establish Schur—Weyl duality between actions resulting P}_k}\left(n symmetric group Sn on Symk(Fn). The construction generalizes any vector λ non-negative integers yielding P}_\lambda}\...

We enhance Gamma, a multiset rewriting language, with a notion of structured multiset. A structured multiset is a set of addresses satisfying speci c relations which can be used in the rewriting rules of the program. A type is de ned by a context-free graph grammar and a structured multiset belongs to a type T if its underlying set of addresses satis es the invariant expressed by the grammar de...

Given a set R of robots, each one located at different vertex an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF) problem. multiset F grid vertices such that |R|=|F|, APF asks for distributed algorithm moves robots so as reach configuration similar F. Similarity means must be disposed regardless translations, rotations, reflections. So far, possible g...

The paper determines the algebraic and logic structure of the multiset semantics of the core patterns of SPARQL. We prove that the fragment formed by AND, UNION, OPTIONAL, FILTER, MINUS and SELECT corresponds precisely to both, the intuitive multiset relational algebra (projection, selection, natural join, arithmetic union and except), and the multiset non-recursive Datalog with safe negation.