On Total Positivity of Catalan-Stieltjes Matrices
نویسندگان
چکیده
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 every minor of A is equal to the sum of the weights of families of nonintersecting paths of the digraph. We have also an analogous result for the minors of a Hankel matrix associated to the first column of a Catalan-Stieltjes matrix.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016