scholarly journals On the r-Central Coefficient Matrices of the Catalan Triangles

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Juan Yin ◽  
Sheng-Liang Yang
Keyword(s):  
Inversion Formula ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula ◽  
Definition Of ◽  
Riordan Array ◽  
Central Coefficient

We introduce the definition of the r-central coefficient matrices of a given Riordan array. Applying this definition and Lagrange Inversion Formula, we can calculate the r-central coefficient matrices of Catalan triangles and obtain some interesting triangles and sequences.

scholarly journals Δ-Cumulants in terms of moments

2018 ◽  
Vol 21 (02) ◽  
pp. 1850012
Author(s):  
Matthieu Josuat-Vergès
Keyword(s):  
Inversion Formula ◽  
Probability Measures ◽  
Combinatorial Formula ◽  
Noncrossing Partitions ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula ◽  
Simple Variant ◽  
Definition Of

The [Formula: see text]-convolution of real probability measures, introduced by Bożejko, generalizes both free and Boolean convolutions. It is linearized by the [Formula: see text]-cumulants, and Yoshida gave a combinatorial formula for moments in terms of [Formula: see text]-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the [Formula: see text]-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida’s formula involving Schröder trees.

scholarly journals A Multivariate Lagrange Inversion Formula for Asymptotic Calculations

10.37236/1371 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Edward A. Bender ◽  
L. Bruce Richmond
Keyword(s):  
Inversion Formula ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula

The determinant that is present in traditional formulations of multivariate Lagrange inversion causes difficulties when one attempts to obtain asymptotic information. We obtain an alternate formulation as a sum of terms, thereby avoiding this difficulty.

Sign in / Sign up

Export Citation Format

Share Document