منابع مشابه
Total positivity in Schubert varieties
We extend the results of [2] on totally positive matrices to totally positive elements in arbitrary semisimple groups. Mathematics Subject Classification (1991). 14M15, 22E46, 15A48.
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The classical regulator R of a number field K is given [F1] by a rapidly convergent series of the form R w = ∞
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An infinite matrix is called totally positive if its minors of all orders are nonnegative. A nonnegative sequence (an)n≥0 is called log-convex (logconcave, resp.) if aiaj+1 ≥ ai+1aj ( aiaj+1 ≤ ai+1aj , resp.) for 0 ≤ i < j . The object of this talk is to study various positivity properties of Riordan arrays, including the total positivity of such a matrix, the log-convexity of the 0th column an...
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It is well established that systems of totally positive blending functions, such as the Bernstein and B-spline bases, preserve monotonicity and convexity and are generally ‘shape preserving’ [9 ]. In this paper we show that total positivity is equivalent to the preservation of all orders of convexity. By a system we understand a sequence of functions (u0, . . . , un) defined on an interval [a, ...
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In this paper we explore the combinatorics of the nonnegative part (G/P )≥0 of a cominuscule Grassmannian. For each such Grassmannian we define Γ -diagrams — certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P )≥0. In the classical cases, we describe Γ -diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2017
ISSN: 0090-5364
DOI: 10.1214/16-aos1478