Proof of a conjecture about unimodal polynomials
نویسندگان
چکیده
منابع مشابه
A Sequence of Unimodal Polynomials
A finite sequence of real numbers {d0, d1, · · · , dm} is said to be unimodal if there exists an index 0 ≤ j ≤ m such that d0 ≤ d1 ≤ · · · ≤ dj and dj ≥ dj+1 ≥ · · · ≥ dm. A polynomial is said to be unimodal if its sequence of coefficients is unimodal. The sequence {d0, d1, · · · , dm} with dj ≥ 0 is said to be logarithmically concave (or log concave for short) if dj+1dj−1 ≤ dj for 1 ≤ j ≤ m − ...
متن کاملA conjecture by Leon Ehrenpreis about zeroes of exponential polynomials
then the ideal (F1, ..., FN) they generate in the Paley-Wiener algebra Ê ′(Rn) is slowly decreasing respect to the Paley-Wiener weight p(z) = log |z| + |Im z|. As a consequence, this ideal is closed in Ê ′(Rn). It coincides with the ideal [I(F1, ..., FN)]loc, which consists of elements in Ê ′(Rn) that belong locally to the ideal generated by F1, ..., FN in the algebra of entire functions in n v...
متن کاملProof of a conjecture about rotation symmetric functions
Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. We prove the conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed in [1], thus the nonlinearity of such kind of functions are determined.
متن کاملA Conjecture about Raising Operators for Macdonald Polynomials
A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Józefiak’s expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser’s formula for partitions with length three.
متن کاملPartial proof of Graham Higman's conjecture related to coset diagrams
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1989
ISSN: 0022-314X
DOI: 10.1016/0022-314x(89)90096-6