Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S3.
Gauss Sums for Symplectic Groups Over a Finite Field.
Gauss sums for O⁻(2n,q)
Exponential sums for symplectic groups and their applications
Exponential sums for O¯(2n,q) and their applications
Sums for U(2n,q²) and their applications
Association schemes and MacWilliams dualities for generalized Niederreiter-Rosenbloom-Tsfasman posets
Let P be a poset on the set [m]×[n], which is given as the disjoint sum of posets on ’columns’ of [m]×[n], and let P̌ be the dual poset of P. Then P is called a generalized Niederreiter-Rosenbloom-Tsfasman poset (gNRTp) if all further posets on columns are weak order posets of the ’same type’. Let G (resp. Ǧ) be the group of all linear automorphisms of the space preserving the P-weight (resp. P̌-weight). We define two partitions of , one consisting of ’P-orbits’ and the other of ’P̌-orbits’....
Gauss sums for O⁺(2n,q)
Gauss sums for orthogonal groups over a finite field of characteristic two
Identities arising from higher-order Daehee polynomial bases
Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.
Some identities of degenerate special polynomials
In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.
Fully degenerate poly-Bernoulli numbers and polynomials
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
Fourier series of functions involving higher-order ordered Bell polynomials
In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
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