Enumeration formulas for generalized q-Euler numbers

Jang Soo Kim

doi:10.1016/j.aam.2012.07.001

Enumeration formulas for generalized q-Euler numbers

Jang Soo Kim

University of Minnesota Twin Cities

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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=± ^qr for any integer r. Special cases of our latter formula include the formula of the q-Euler number recently found by Josuat-Vergès and Touchard-Riordans formula.

Original language	English
Pages (from-to)	326-350
Number of pages	25
Journal	Advances in Applied Mathematics
Volume	49
Issue number	3-5
DOIs	https://doi.org/10.1016/j.aam.2012.07.001
State	Published - Sep 2012
Externally published	Yes

Keywords

Continued fractions
Euler numbers
Touchard-Riordans formula

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10.1016/j.aam.2012.07.001

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abstract = "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=± qr for any integer r. Special cases of our latter formula include the formula of the q-Euler number recently found by Josuat-Verg{\`e}s and Touchard-Riordans formula.",

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AB - 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=± qr for any integer r. Special cases of our latter formula include the formula of the q-Euler number recently found by Josuat-Vergès and Touchard-Riordans formula.

KW - Continued fractions

KW - Euler numbers

KW - Touchard-Riordans formula

UR - https://www.scopus.com/pages/publications/84867886307

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

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ER -

Enumeration formulas for generalized q-Euler numbers

Abstract

Keywords

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