23 citations · 30 across the 5 of their papers we have counts for
5 papers
Generating functions for plateaus in Motzkin paths
Dan Drake, Ryan Gantner
A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for p…
Bijections from weighted Dyck paths to Schroeder paths
Dan Drake
Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schroeder paths, is the same as the weight o…
Higher order matching polynomials and d-orthogonality
Dan Drake
We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating fu…
-distant crossings and nestings of matchings and partitions
Dan Drake, Jang Soo Kim
We define and consider k-distant crossings and nestings for matchings and set partitions, which are a variation of crossings and nestings in which the distance between vertices is…
The combinatorics of associated Hermite polynomials
Dan Drake
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial inte…