We present a characterization of eigenvalue inequalities between two Hermitian matrices
by means of inertia indices. As applications, we deal with some classical eigenvalue …

The Delannoy numbers d ( n , k ) count the number of lattice paths from ( 0 , 0 ) to ( n − k , k )
using steps ( 1 , 0 ) , ( 0 , 1 ) and ( 1 , 1 ) . We show that the zeros of all Delannoy …

Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy
numbers. It turns out that Delannoy matrix, Pascal matrix, and Fibonacci matrix are all special …

The Motzkin numbers count the number of lattice paths which go from ( 0 , 0 ) to ( n , 0 )
using steps ( 1 , 1 ) , ( 1 , 0 ) and ( 1 , − 1 ) and never go below the x -axis. Let M n , k be the …

… LILI MU 1 AND SAI-NAN ZHENG … Zheng, On the total positivity of Delannoy-like
triangles, J. Integer Seq. 20 (2017), 17.1.6. … Zheng, S.-P. Yuan and T.-…

By presenting Riordan matrix as a triangle, the central coefficients are entries in the central
column. Starting at the central column, the r‐shifted central coefficients are entries in column r …

… Sai-nan Zheng School of Mathematical Sciences Dalian University of Technology Dalian, …
[18] SL Yang, SN Zheng, SP Yuan, and TX He, Schröder matrix as inverse of Delannoy matrix, …

Using the exponential Riordan arrays, we show that a variation of the generalized Bessel
polynomial sequence is of Sheffer type, and we obtain a determinant formula for the …

In this paper, using the production matrix of a Riordan array, we obtain a recurrence relation
for polynomial sequence associated with the Riordan array, and we also show that the …

A Riordan array $$R=[r_{n,k}]_{n,k\ge 0}$$ R = [ r n , k ] n , k ≥ 0 can be characterized by two
sequences $$A=(a_n)_{n\ge 0}$$ A = ( a n ) n ≥ 0 and $$Z=(z_n)_{n\ge 0}$$ Z = ( z n ) n …