منابع مشابه
On Total Positivity of Catalan-Stieltjes Matrices
Recently Chen-Liang-Wang (Linear Algebra Appl. 471 (2015) 383–393) present some sufficient conditions for the total positivity of Catalan-Stieltjes matrices. Our aim is to provide a combinatorial interpretation of their sufficient conditions. More precisely, for any Catalan-Stieltjes matrix A we construct a digraph with a weight, which is positive under their sufficient conditions, such that ev...
متن کاملNote on Total Positivity for a Class of Recursive Matrices
In this note, we study the total positivity of a class of infinite recursive matrices that depend on three infinite sets of independent variables and on an integer parameter. We give a simple algebraic proof and provide a few examples.
متن کاملPositivity and Conditional Positivity of Loewner Matrices
We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...
متن کاملMultivariate Fuss-Narayana Polynomials and their Application to Random Matrices
It has been shown recently that the limit moments of W (n) = B(n)B∗(n), where B(n) is a product of p independent rectangular random matrices, are certain homogeneous polynomials Pk(d0, d1, . . . , dp) in the asymptotic dimensions of these matrices. Using the combinatorics of noncrossing partitions, we explicitly determine these polynomials and show that they are closely related to polynomials w...
متن کاملTotal positivity of Riordan arrays
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.01.012