Parametric combinatorial problems and methods of their research

Four combinatorial problems parametrized by multiplicity r of an element of base multiset are considered: distribution of indexes vp-monotonous permutations, the generalized Gessel - Stanley permutations and the generalized Baclawski - Edelman partially ordered sets, the generalized Stirling numbers and the generalized partially ordered sets of the partitions, the generalized statistics and generalized Eulerian polynomials. For research of these problems various methods are involved.