Enumerative combinatorics
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
Riordan arrays and combinatorial sums
Discrete Mathematics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
European Journal of Combinatorics
Some linear recurrences and their combinatorial interpretation by means of regular languages
Theoretical Computer Science
Discrete Mathematics
Matrix identities on weighted partial Motzkin paths
European Journal of Combinatorics
The Sheffer group and the Riordan group
Discrete Applied Mathematics
Proper generating trees and their internal path length
Discrete Applied Mathematics
Ultrametrics, Banach's fixed point theorem and the Riordan group
Discrete Applied Mathematics
Riordan group involutions and the Δ-sequence
Discrete Applied Mathematics
The hitting time subgroup, Łukasiewicz paths and Faber polynomials
European Journal of Combinatorics
Minors of a class of Riordan arrays related to weighted partial Motzkin paths
European Journal of Combinatorics
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One of the cornerstone ideas in mathematics is to take a problem and to look at it in a bigger space. In this paper we examine combinatorial sequences in the context of the Riordan group. Various subgroups of the Riordan group each give us a different view of the original sequence. In many cases this leads to both a combinatorial interpretation and to ECO rewriting rules. In this paper we will concentrate on just four of the subgroups of the Riordan group to demonstrate some of the possibilities of this approach.