$m$-submultisets and $m$-permutations of multisets elements

The article is devoted to two classical combinatorial problems on multisets, which in the existing literature are given unjustifiably little space. Namely, calculation of number all submultisets power $m$ for an arbitrary multiset and $m$-permutations such multisets. first problem closely related width a partially ordered set with inclusion $\subseteq$. contains some important classes Combinatorial proofs $m$-submultisets elements considered. In article, basis generatrix method, economical algorithms calculating constructed. paper also provides brief overview results that this area research.