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A probabilistic interpretation of the Gaussian binomial coefficients

Part of: Stochastic processes Algebraic combinatorics

Published online by Cambridge University Press:  30 November 2017

Takis Konstantopoulos  and
Linglong Yuan
Takis Konstantopoulos*
Affiliation:
Uppsala University
Linglong Yuan*
Affiliation:
Xi'an Jiaotong-Liverpool University
*
* Postal address: Department of Mathematics, Uppsala University, SE-75106 Uppsala, Sweden. Email address: [email protected]
** Postal address: Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, 111 Ren'ai Road, Suzhou, 215123, P. R. China.
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Abstract

We present a stand-alone simple proof of a probabilistic interpretation of the Gaussian binomial coefficients by conditioning a random walk to hit a given lattice point at a given time.

Keywords

Gaussian binomial coefficientq-binomialrandom walk

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 05E99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1295 - 1298
Copyright
Copyright © Applied Probability Trust 2017 

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References

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