The notion of a p-Riordan graph generalizes that of a Riordan graph, which, in turn, generalizes the notions of a Pascal graph and a Toeplitz graph. In this paper we introduce the notion of a p-Riordan word, and show how to encode p-Riordan graphs by p-Riordan words. For special important cases of Riordan graphs (the case p=2) and oriented Riordan graphs (the case p=3) we provide alternative encodings in terms of pattern-avoiding permutations and certain balanced words, respectively. As a bi-product of our studies, we provide an alternative proof of a known enumerative result on closed walks in the cube.
|Journal||Graphs and Combinatorics|
|Publication status||Accepted/In press - 1 Sep 2020|
- Riordan graph
- p-Riordan graph
- p-Riordan word
- permutation pattern
- balanced word