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Korean Mathematical Society (대한수학회)
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AN ALTERNATIVE q-ANALOGUE OF THE RUCINSKI-VOIGT NUMBERS

  • Bent-Usman, Wardah M. (Department of Mathematics Mindanao State University-Main Campus) ;
  • Dibagulun, Amerah M. (Department of Mathematics Mindanao State University-Main Campus) ;
  • Mangontarum, Mahid M. (Department of Mathematics Mindanao State University-Main Campus) ;
  • Montero, Charles B. (Department of Mathematics Mindanao State University-Main Campus)
  • Received : 2017.09.10
  • Accepted : 2018.01.10
  • Published : 2018.10.31
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Abstract

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.

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References

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