منابع مشابه
Total 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...
متن کاملGeneralized Riordan arrays
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...
متن کاملComplementary Riordan arrays
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.
متن کاملSequence characterization of Riordan arrays
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...
متن کاملMatrix Characterizations of Riordan Arrays
Here we discuss two matrix characterizations of Riordan arrays, P -matrix characterization and A-matrix characterization. P -matrix is an extension of the Stieltjes matrix defined in [25] and the production matrix defined in [7]. By modifying the marked succession rule introduced in [18], a combinatorial interpretation of the P -matrix is given. The P -matrix characterizations of some subgroups...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2014.11.009