• Korean Journal of Mathematics
• /
• v.15 no.2
• /
• pp.177-183
• /
• 2007

In this paper, we study the Riordan matrices with the A-sequence (1,1,...,1,0,...) where 1's appear in m times. As a result, we obtain new Riordan matrices and give their lattice path interpretations.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.147-154
• /
• 2009

In this paper, we consider a new sequence called by the C-sequence of the Riordan array. It allows us to find a simple proof for several combinatorial identities. Further, we prove that a C-sequence characterizes Bell subgroup of the Riordan group.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.187-199
• /
• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $b^{(r)}_n$ and $b^{(r+1)}_n$.