Normal approximations for descents and inversions of permutations of the set {1, 2, . . . , n} are well known. We consider the number of inversions of a permutation π(1), π(2), . . . , π(n) of a multiset with n elements, which is the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). The number of descents is the number of i in the range 1 ≤ i < n such that π(i) > π(i + 1). We prove tha...

Two kinds of multiset automata with a storage attached, varying only in their ability of testing the storage for emptiness, are introduced, as well as normal forms. Their accepting power and relation to other multiset languages classes is investigated.

we extend some results of Lempel and Restive on multiset decipherable codes to set decipherable codes. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Codes, Unique decipherability, Multiset decipherability, Dominoes, Set decipherability.

We prove that, given a nite set of words S, there exists at most one (normalized) multiset P such that S is the shuue of the words in P. The multiset P is eeectively computable.

Abstract Fuzzy multiset finite automata with output represent fuzzy version of (with output) working over multisets. This paper introduces Mealy-like, Moore-like, and compact automata. Their mutual transformations are described to prove their equivalent behaviours. Furthermore, various variants reduced studied where the reductions directed decrease number components (like initial distribution, ...

general, any n-sequence determines a multiset of (= n!/k!(n-k)!) k-sequences. "J Suppose, conversely, that we are given a multiset 01 k-sequences. Does that multiset come from some sequence? If so, is the source sequence unique? Such questions are reminiscent of the problem of reconstructing graphs from vertex-deleted sub raphs, which has received a great deal of attention in the last twent yea...