DMTCS
2010
13 years 1 months ago
2010
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...
JCT
2010
13 years 3 months ago
2010
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...
COMBINATORICS
1999
13 years 4 months ago
1999
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...
COMBINATORICS
1999
13 years 4 months ago
1999
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. ...
DM
1998
13 years 4 months ago
1998
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...
DM
1998
13 years 4 months ago
1998
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 ...
COMBINATORICS
1998
13 years 4 months ago
1998
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...
COMBINATORICS
2002
13 years 4 months ago
2002
Based on Sch
COMBINATORICS
2004
13 years 4 months ago
2004
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 ...
PE
2008
Springer
13 years 4 months ago
2008
Springer
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 ...