On a problem of Turan about polynomials

On a Two-Sided Turan Problem

Given positive integers n, k, t, with 2 ≤ k ≤ n, and t < 2, let m(n, k, t) be the minimum size of a family F of nonempty subsets of [n] such that every k-set in [n] contains at least t sets from F , and every (k − 1)-set in [n] contains at most t− 1 sets from F . Sloan et. al [11] determined m(n, 3, 2) and Füredi et. al [6] studied m(n, 4, t) for t = 2, 3. We consider m(n, 3, t) and m(n, 4, t) ...

Jensen Polynomials and the Turan and Laguerre Inequalities

1231-1235 Turan LAJP 3348:Turan

Ismayil YILMAZ 1, Ismail DEMIRYILMAZ 2, Mehmet I. TURAN 3*, Bahadır SULEYMAN 4, Isil S. TURAN 5, Durdu ALTUNER 4, Hamit H. ALP 6 & Halis SULEYMAN 4 1 Erzincan University, Faculty of Medicine, Department of Surgery, Erzincan, Turkey 2 Ibni Sina Hospital, Department of General Surgery, Kayseri, Turkey 3 Diyarbakir Research and Educational Hospital, Department of Pediatric Neurology, Diyarbakir, T...

On a problem of Diophantus with polynomials

Let m ≥ 2 and k ≥ 2 be integers and let R be a commutative ring with a unit element denoted by 1. A k-th power diophantine m-tuple in R is an m-tuple (a1, a2, . . . , am) of non-zero elements of R such that aiaj +1 is a k-th power of an element of R for 1 ≤ i < j ≤ m. In this paper, we investigate the case when k ≥ 3 and R = K[X], the ring of polynomials with coefficients in a field K of charac...

On a Problem concerning Permutation Polynomials

Let S(f) denote the set of integral ideals / such that / is a permutation polynomial modulo i", where / is a polynomial over the ring of integers of an algebraic number field. We obtain a classification for the sets S which may be written in the form S(f). Introduction. A polynomial f(x) with coefficients in a commutative ring R is said to be a permutation polynomial modulo an ideal I oi R (abb...