### Abstract

Stirling numbers of the second kind, S(n, r), denote the number of partitions of a finite set of size n into r disjoint nonempty subsets. The aim of this short article is to shed some light on the generating functions of these numbers by deriving them probabilistically. We do this by linking them to Markov chains related to the classical coupon collector problem; coupons are collected in discrete time (ordinary generating function) or in continuous time (exponential generating function). We also review the shortest possible combinatorial derivations of these generating functions.

Original language | English (US) |
---|---|

Pages (from-to) | 82-87 |

Number of pages | 6 |

Journal | Mathematical Scientist |

Volume | 43 |

Issue number | 2 |

State | Published - Dec 1 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Materials Science(all)

### Cite this

*Mathematical Scientist*,

*43*(2), 82-87.

}

*Mathematical Scientist*, vol. 43, no. 2, pp. 82-87.

**The generating functions of stirling numbers of the second kind derived probabilistically.** / Kesidis, George; Konstantopoulos, Takis; Zazanis, Michael A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The generating functions of stirling numbers of the second kind derived probabilistically

AU - Kesidis, George

AU - Konstantopoulos, Takis

AU - Zazanis, Michael A.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Stirling numbers of the second kind, S(n, r), denote the number of partitions of a finite set of size n into r disjoint nonempty subsets. The aim of this short article is to shed some light on the generating functions of these numbers by deriving them probabilistically. We do this by linking them to Markov chains related to the classical coupon collector problem; coupons are collected in discrete time (ordinary generating function) or in continuous time (exponential generating function). We also review the shortest possible combinatorial derivations of these generating functions.

AB - Stirling numbers of the second kind, S(n, r), denote the number of partitions of a finite set of size n into r disjoint nonempty subsets. The aim of this short article is to shed some light on the generating functions of these numbers by deriving them probabilistically. We do this by linking them to Markov chains related to the classical coupon collector problem; coupons are collected in discrete time (ordinary generating function) or in continuous time (exponential generating function). We also review the shortest possible combinatorial derivations of these generating functions.

UR - http://www.scopus.com/inward/record.url?scp=85059664217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059664217&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85059664217

VL - 43

SP - 82

EP - 87

JO - Mathematical Scientist

JF - Mathematical Scientist

SN - 0312-3685

IS - 2

ER -