PARAMETRIC COMBINATORY PROBLEMS AND METHODS OF THEIR RESEARCH

Bondarenko Leonid Nikolaevich, Candidate of engineering sciences, associate professor, sub-department of discrete mathematics, Penza State University, dm@pnzgu.ru
Sharapova Marina Leonidovna, Assistant, sub-department of general topology and geometry, Moscow State University named after M. V. Lomonosov, dm@pnzgu.ru

519.1

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.

multiset, statistic, generating function, vp-monotonous permutations, Gessel – Stanley permutations, Baclawski – Edelman posets, Stirling numbers, posets partitions, Eulerian polynomials.