منابع مشابه
2 00 5 Schur Positivity and Schur Log - Concavity
We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An alternative proof of this result is provided. We also give an intriguing log-concavity property of Schur functions. 1. Schur positivity conjectures The ring of...
متن کامل. C O ] 1 4 Se p 20 05 SCHUR POSITIVITY AND SCHUR LOG - CONCAVITY
We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. We include an alternative derivation of this result directly from Haiman’s work on Schur positive immanants. Our results imply an intriguing log-concavity propert...
متن کاملThe Schur Cone and the Cone of Log Concavity
Let {h1, h2, . . . } be a set of algebraically independent variables. We ask which vectors are extreme in the cone generated by hihj − hi+1hj−1 (i ≥ j > 0) and hi (i > 0). We call this cone the cone of log concavity. More generally, we ask which vectors are extreme in the cone generated by Schur functions of partitions with k or fewer parts. We give a conjecture characterizing which vectors are...
متن کاملSchur-convexity and Schur-geometrically concavity of Gini means
The monotonicity and the Schur-convexity with parameters (s, t) in R2 for fixed (x, y) and the Schur-convexity and the Schur-geometrically convexity with variables (x, y) in R++ for fixed (s, t) of Gini mean G(r, s;x, y) are discussed. Some new inequalities are obtained.
متن کاملLog-concavity and LC-positivity
A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑n k=r a(n, k)q k is q-log-concave. It is double LC-positive if both triangles {a(n, k)} and {a(n, n − k)} are LC-positive. We show that if {a(n, k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by zn = ∑n k=0 a(n, k)xk, and if {a(n, ...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2007
ISSN: 1080-6377
DOI: 10.1353/ajm.2007.0045