Münster J. of Math. 3 (2010), 129--150
Dominique Foata, Guo-Niu Han
DOUBLOONS AND q-SECANT NUMBERS
Abstract.
Based on the evaluation at t=-1 of the generating polynomial
for the hyperoctahedral group by the number of descents,
an observation recently made by Hirzebruch,
a new q-secant number is derived by working with the
Chow-Gessel q-polynomial involving the flag major index.
Using the doubloon combinatorial model we show that
this new q-secant number is a polynomial with
positive integral coefficients,
a property apparently hard to prove by analytical methods.
foata at unistra dot fr,
guoniu dot han at unistra dot fr
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