### Annals of
Combinatorics 4 (2000) 195-197
A Bijective Answer to a
Question of Zvonkin
Richard Ehrenborg
Department of Mathematics, Royal Institute of Technology,
S-100 44 Stockholm, Sweden
jrge@math.kth.se
Received March 17, 2000
**AMS Subject Classification**:
05A15, 60C05
**Abstract.** The purpose of
this note is to give a bijective proof of the identity
where are independent identically distributed
normal random variables with mean 0 and variance 1. The bijection
is obtained by combining a bijection of Gessel and a bijection of
Ehrenborg with the interpretation that the moments of the normal
distribution count the number of matchings.
**Keywords**: normal zero-one
random variables, Vandermonde product, tournaments, matchings
**References**
1. R. Ehrenborg,* The Hankel determinant of exponential polynomials*, Amer. Math. Monthly
107 (2000) 557–560.
2. I. Gessel, *Tournaments and Vandermonde’s determinant*, J. Graph Theory 3 (1979) 305–307.
3. A. Zvonkin, *Matrix integrals and map enumeration*: *An accessible introduction*, Math. Comput.
Modelling 26 (1997) 281–304.
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