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A probabilistic interpretation of the Gaussian binomial coefficients

  • Takis Konstantopoulos (a1) and Linglong Yuan (a2)
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.

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Corresponding author
* Postal address: Department of Mathematics, Uppsala University, SE-75106 Uppsala, Sweden. Email address: takiskonst@gmail.com
** Postal address: Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, 111 Ren'ai Road, Suzhou, 215123, P. R. China.
References
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[1] Brent, R. P. and McKay, B. D. (1987). Determinants and ranks of random matrices over ℤ m . Discrete Math. 66, 3549.
[2] Crippa, D. and Simon, K. (1995). q-distributions in random graphs: transitive closure and reduction. Tech. Rep., ETH Zürich.
[3] Crippa, D. and Simon, K. (1997). q-distributions and Markov processes. Discrete Math. 170, 8198.
[4] Gauss, C. F. (1811). Summatio quarundam serierum singularium. In Untersuchungen über höhere Arithmetik (translated by H. Maser), 2nd edn. Chelsea, New York, 1965.
[5] Kac, V. and Cheung, P. (2002). Quantum Calculus. Springer, New York.
[6] O'Connell, N. and Pei, Y. (2013). A q-weighted version of the Robinson–Schensted algorithm. Electron. J. Prob. 18, 95.
[7] Pólya, G. (1969). On the number of certain lattice polygons. J. Combinatorial Theory 6, 102105.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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