In two recent papers, Feigin proved that the Poincaré polynomials of the degenerate flag varieties have a combinatorial interpretation through Dellac configurations, and related them to the q-extended normalized median Genocchi numbers c̄n(q) introduced by Han and Zeng, mainly by geometric considerations. In this paper, we give combinatorial proofs of these results by constructing statistic-pres...

Among a remarkably large number of various extensions polynomials and numbers, diverse introductions new in this paper, we choose to introduce two generalizations some extended Bernoulli numbers by using the Mittag–Leffler function confluent hypergeometric function. Then, investigate certain properties formulas these newly introduced such as explicit representations, addition formulas, integral...

Motivated by Kurt’s work [Filomat 30 (4) 921-927, 2016], we …rst consider a class of a new generating function for (p; q)-analog of Apostol type polynomials of order including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order . By making use of their generating function, we derive some useful identities. We also introduce (p; q)-analog of Stirling numbers of second kind...

In [1], Cangul-Ozden-Simsek constructed a q-Genocchi numbers of higher order and gave Witt’s formula of these numbers by using a p-adic fermionic integral on Zp. In this paper, we give another constructions of a q-Euler and Genocchi numbers of higher order, which are different than their q-Genocchi and Euler numbers of higher order. By using our q-Euler and Genocchi numbers of higher order, we ...

Abstract Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation this, in this paper, we introduce degenerate poly-Bell polynomials emanating from polyexponential functions which are called when $\lambda \rightarrow 0$ ?...

We establish congruences for higher order Euler polynomials modulo 720. apply this result constructing analogues of Stern secant numbers $E_{4n}\equiv 5(\mathrm{mod}\ 60), E_{4n+2}\equiv -1(\mathrm{mod}\ 60)$ to tangent and Genocchi numbers. prove that satisfy the following $E_{4n+1}\equiv 16(\mathrm{mod}\ 720)$, $E_{4n+3}\equiv -272(\mathrm{mod}\ 720)$. 12-periodic property 45.