A Criterion for Unimodality
نویسندگان
چکیده
منابع مشابه
A Criterion for Unimodality
We show that if P (x) is a polynomial with nondecreasing, nonnegative coefficients, then the coefficient sequence of P (x+ 1) is unimodal. Applications are given.
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We prove that if P (x) is a polynomial with nonnegative nondecreasing coefficients and n is a positive integer, then P (x + n) is unimodal. Applications and open problems are presented.
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It is well known that the principal specialization of the Schur function, sλ(1, q, . . . , q ), is a unimodal polynomial. A brief representation theoretic proof consists in identifying sλ(1, q, . . . , q ) as the character of a homogeneous polynomial representation of GL(2,C) evaluated at diag(1, q), see [3, p. 67]. Recently O’Hara gave a combinatorial proof [4] of the unimodality of the Gaussi...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1999
ISSN: 1077-8926
DOI: 10.37236/1442