2020/09/03 by Iamthong, Kittitat, Jung, Ji-Hwan, Kitaev, Sergey
#05A05 #05A15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2009.01410
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.