On the Basis Polynomials in the Theory of Permutations with Prescribed Up-down Structure
نویسنده
چکیده
We study the polynomials which enumerate the permutations π = (π1, π2, . . . , πn) of the elements 1.2, . . . , n with the condition π1 < π2 < . . . < πn−m(or π1 > π2 > . . . > πn−m) and prescribed up-down points n−m,n−m+1, . . . , n− 1 in view of an important role of these polynomials in theory of enumeration the permutations with prescribed up-down structure similar to the role of the binomial coefficients in the enumeration of the subsets of a finite set satisfying some restrictions.
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تاریخ انتشار 2008