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An alternative $q$-analogue of the Ruci\'nski-Voigt numbers

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In this paper, we define an alternative $q$-analogue of the Ruci\'nski-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be $q$-deformations of similar properties for the Ruci\'nski-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of $A$-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the Ruci\'nski-Voigt and the $q$-Ruci\'nski-Voigt numbers.

Abstract

In this paper, we define an alternative $q$-analogue of the Ruci\'nski-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be $q$-deformations of similar properties for the Ruci\'nski-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of $A$-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the Ruci\'nski-Voigt and the $q$-Ruci\'nski-Voigt numbers.

참고문헌 (33)

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