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AN ALTERNATIVE q-ANALOGUE OF THE RUCINSKI-VOIGT NUMBERS
Bent-Usman, Wardah M.,Dibagulun, Amerah M.,Mangontarum, Mahid M.,Montero, Charles B. Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4
In this paper, we define an alternative q-analogue of the $Ruci{\acute{n}}ski$-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 $Ruci{\acute{n}}ski$-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 $Ruci{\acute{n}}ski$-Voigt and the q-$Ruci{\acute{n}}ski$-Voigt numbers.