m-submultisets and m-permutations of multisets elements

TL;DR

This paper explores classes of multisets, providing combinatorial proofs and algorithms for counting m-submultisets and m-permutations, and generalizes Pascal's triangle for multisets.

Contribution

It introduces new combinatorial proofs and algorithms for multiset enumeration, extending classical combinatorial structures like Pascal's triangle.

Findings

Developed algorithms for counting m-submultisets and m-permutations

Provided combinatorial proofs for multiset enumeration problems

Generalized Pascal's triangle for multisets

Abstract

The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In particular, the Pascal triangle is generalized in the case of multisets.