Using the saddle point method, we obtain from the generating function of the Stirling numbers of the first kind n j and Cauchy's integral formula, asymptotic results in centr...
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that ha...
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
Kasteleyn stated that the generating function of the perfect matchings of a graph of genus g may be written as a linear combination of 4g Pfaffians. Here we prove this statement. ...
We study basis partitions, introduced by Hansraj Gupta in 1978. For this family of partitions, we give a recurrence, a generating function, identities relating basis partitions to...
Jennifer M. Nolan, Carla D. Savage, Herbert S. Wil...
We introduce three deÿnitions of q-analogs of Motzkin numbers and illustrate some combinatorial interpretations of these q-numbers. We relate the ÿrst class of q-numbers to the ...
Elena Barcucci, Alberto Del Lungo, Jean-Marc Fedou...
Using Zeilberger’s factorization of two-stack-sortable permutations, we write a functional equation — of a strange sort — that defines their generating function according t...
In this paper, we examine partitions classified according to the number r() of odd parts in and s() the number of odd parts in , the conjugate of . The generating function for ...
We present the transient analysis of the system content in a two-class discrete-time MX /D/1 priority queue. In particular, we derive an expression for the generating function of ...