arXiv subjects
Publications and source records attributed to Mahid M. Mangontarum.
In this paper, the unified generalized $q$-Stirling matrices are defined in terms of the $q$-analogues of the unified generalized Stirling numbers. Several matrix relations involving these matrices are derived, and matrix decompositions of the unified generalized $q$-Stirling matrices are established.
In this paper, we established some integral formulas for and involving the noncentral Tanny-Dowling polynomials. These formulas are shown to be generalizations of some known results on the classical geometric polynomials.
In this paper, we extend the r-Dowling polynomials to their bivariate forms. Several properties that generalize those of the bivariate Bell and r-Bell polynomials are established. Finally, we obtain two forms of generalized Spivey's formula.
In this paper, we derive formulas for the translated Whitney-Lah numbers and show that they are generalizations of already-existing identities of the classical Lah numbers. q-analogues of the said formulas are also obtained for the case of the translated q-Whitney numbers.
In this paper, we establish some formulas for the noncentral Tanny-Dowling polynomials including sums of products and explicit formulas which are shown to be generalizations of known identities. Other important results and consequences are also discussed and presented.
In this paper, a generalized recurrence relation for the $r$-Whitney numbers of the second kind is derived using as framework the operators $X$ and $D$ satisfying the commutation relation $DX-XD=1$. This recurrence relation is shown to be a generalization of the well-known Spivey's Bell number. Moreover, several other identities generalizing Spivey's Bell number formula are obtained.
This paper introduces an alternative form of the derivation of Spivey's Bell number formula which involves the $q$-Boson operators $a$ and $a^{\dagger}$. Furthermore, a similar formula for the case of the $(q,r)$-Dowling polynomials is obtained, and is shown to produce a generalization of the latter.
The $(q,r)$-Whitney numbers were recently defined in terms of the $q$-Boson operators, and several combinatorial properties which appear to be $q$-analogues of similar properties were studied. In this paper, we obtain elementary and complete symmetric polynomial forms for the $(q,r)$-Whitney numbers, and give combinatorial interpretations in the context of $A$-tableaux. We also obtain convolution-type identities using the combinatorics of $A$-tableaux. Lastly, we present applications and theorems related to discrete $q$-distributions.