Journal of Combinatorics

Volume 8 (2017)

Number 1

Moments of matching statistics

Pages: 1 – 27



Niraj Khare (Carnegie Mellon University, Doha, Qatar)

Rudolph Lorentz (Texas A&M University, Doha, Qatar)

Catherine H. Yan (Department of Mathematics, Texas A&M University, College Station, Tx., U.S.A.)


We show that for a large family of combinatorial statistics on perfect matchings, the moments can be expressed as a linear combination of double factorials with constant coefficients. This gives a stronger analogous result of Chern, Diaconis, Kane and Rhoades on statistics of set partitions, in which case the moments can be expressed as linear combinations of shifted Bell numbers, but with polynomial coefficients.


matching, statistics

2010 Mathematics Subject Classification

05A15, 05A18, 62J05

Published 2 December 2016