Some (counter)examples on totally positive Riordan arrays
نویسندگان
چکیده
منابع مشابه
On Some Alternative Characterizations of Riordan Arrays
We give several new characterizations of Riordan Arrays, the most important of which is: if fd n;k g n;k2N is a lower triangular array whose generic element d n;k linearly depends on the elements in a well-deened though large area of the array, then fd n;k g n;k2N is Riordan. We also provide some applications of these characterizations to the lattice path theory.
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In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to cn is an infinite, lower triangular array determined by the pair (g(t), f(t)) and has the generic element dn,k = [t/cn]g(t)(f(t))/ck, where cn is a fixed sequence of non-zero constants with c0 = 1. We demonstrate that the generalized Riordan arrays have similar properties to those of the class...
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Recently, the concept of the complementary array of a Riordan array (or recursive matrix) has been introduced. Here we generalize the concept and distinguish between dual and complementary arrays. We show a number of properties of these arrays, how they are computed and their relation with inversion. Finally, we use them to find explicit formulas for the elements of many recursive matrices.
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We study a super group of the group of Riordan arrays, where the elements of the group are given by a triple of power series. We show that certain subsets are subgroups, and we identify a normal subgroup whose cosets correspond to Riordan arrays. We give an example of an almost-Riordan array that has been studied in the context of Hankel and Hankel plus Toepliz matrices, and we show that suitab...
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In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the Aand Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the Aand Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtaine...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2020
ISSN: 0024-3795
DOI: 10.1016/j.laa.2020.02.021