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DMTCS
2010
128views Mathematics» more  DMTCS 2010»
8 years 25 days ago
Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach
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...
Guy Louchard
JCT
2010
83views more  JCT 2010»
8 years 1 months ago
Families of prudent self-avoiding walks
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...
Mireille Bousquet-Mélou
COMBINATORICS
1999
85views more  COMBINATORICS 1999»
8 years 3 months ago
Permutation Patterns and Continued Fractions
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
COMBINATORICS
1999
80views more  COMBINATORICS 1999»
8 years 3 months ago
On the Theory of Pfaffian Orientations. I. Perfect Matchings and Permanents
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. ...
Anna Galluccio, Martin Loebl
DM
1998
80views more  DM 1998»
8 years 3 months ago
Basis partitions
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...
DM
1998
66views more  DM 1998»
8 years 3 months ago
Steep polyominoes, q-Motzkin numbers and q-Bessel functions
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...
COMBINATORICS
1998
88views more  COMBINATORICS 1998»
8 years 3 months ago
Multi-statistic enumeration of two-stack sortable permutations
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...
Mireille Bousquet-Mélou
COMBINATORICS
2004
70views more  COMBINATORICS 2004»
8 years 3 months ago
On a Partition Function of Richard Stanley
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 ...
George E. Andrews
PE
2008
Springer
106views Optimization» more  PE 2008»
8 years 3 months ago
Time-dependent performance analysis of a discrete-time priority queue
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 ...
Joris Walraevens, Dieter Fiems, Herwig Bruneel
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