The inverse relations to some generating functions of permutations

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Simple permutations and algebraic generating functions

A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations has an algebraic generating function. We extend this result to enumerate permutations in such a class satisfying additional properties, e.g., the even permutations, the involutions, the permutations av...

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Some bilinear generating functions.

In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre,...

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Generating Functions for the Number of Permutations with Limited Displacement

Let V (d, n) be the number of permutations p of {1, 2, . . . , n} that satisfy |pi−i| 6 d for all i. Generating functions for V (d, n), for fixed d, are given.

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ژورنال

عنوان ژورنال: Časopis pro pěstování matematiky

سال: 1967

ISSN: 0528-2195

DOI: 10.21136/cpm.1967.117610