We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to...
We find, in the form of a continued fraction, the generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to ext...
Aaron Robertson, Herbert S. Wilf, Doron Zeilberger
Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues...
Let fr n(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12 . . . k, and let Fr(x; k) and F (x, y; k) be the generating functions d...