Sung-Soo Pyo

THE n-TH TWISTED CHANGHEE POLYNOMIALS AND NUMBERS

The Changhee polynomials and numbers are introduced in (6). Some interesting identities and properties of those polynomials are derived from umbral calculus (see (6)). In this paper, we consider Witt- type formula for the n-th twisted Changhee numbers and polynomials and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials.

Vector majorization via positive definite matrices

Abstract It is well known that for real n -vectors y and x, y majorizes x if and only if A y = x for some doubly stochastic matrix A of order n . If the components of each of y and x are in nonincreasing order, then it is known that the matrix A can be chosen to be positive semidefinite symmetric. We characterize when there is a positive definite doubly stochastic matrix A such that A y = x.

Doubly stochastic matrices whose powers eventually stop

Abstract In this note we characterize doubly stochastic matrices A whose powers A,A 2 ,A 3 ,… eventually stop, i.e., A p =A p+1 =⋯ for some positive integer p. The characterization enables us to determine the set of all such matrices.

Degenerate Cauchy numbers of the third kind

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

Identities between harmonic, hyperharmonic and Daehee numbers

In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number. In addition, we use this differential equation to obtain some identities in which the hyperharmonic numbers and the Daehee numbers are involved.