Jang Soo Kim
Published 2011-04-23, updated 2012-10-19Version 3
We find an enumeration formula for a $(t,q)$-Euler number which is a generalization of the $q$-Euler number introduced by Han, Randrianarivony, and Zeng. We also give a combinatorial expression for the $(t,q)$-Euler number and find another formula when $t=\pm q^r$ for any integer $r$. Special cases of our latter formula include the formula of the $q$-Euler number recently found by Josuat-Verg\`es and Touchard-Riordan's formula.
Comments: 21 pages, 12 figures
Journal: Advances in Applied Mathematics 49 (2012) 326-350
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