65 citations · 145 across the 18 of their papers we have counts for
23 papers
Quantized rational chip-firing
Spencer Backman, Nicholas A. Loehr, Gregory S. Warrington
This article introduces a quantized chip-firing model with close connections to the theory of rational lattice paths and rational parking functions. Given a graph with a sink and p…
A local framework for proving combinatorial matrix inversion theorems
Aditya Khanna, Nicholas A. Loehr
Combinatorial transition matrices arise frequently in the theory of symmetric functions and their generalizations. The entries of such matrices often count signed, weighted combina…
Transition matrices and Pieri-type rules for polysymmetric functions
Aditya Khanna, Nicholas A. Loehr
Asvin G and Andrew O'Desky recently introduced the graded algebra P of polysymmetric functions as a generalization of the algebra of symmetric functions. This article develo…
Skeletal generalizations of Dyck paths, parking functions, and chip-firing games
Spencer Backman, Cole Charbonneau, Nicholas A. Loehr +3
For , we introduce a family of -skeletal paths which are counted by the -th Catalan number for each , and specialize to Dyck paths when . We simila…
Bijective proofs of some coinversion identities related to Macdonald polynomials
Nicholas A. Loehr
This paper gives bijective proofs of some novel coinversion identities first discovered by Ayyer, Mandelshtam, and Martin (arxiv:2011.06117) as part of their proof of a new combina…
A rooted variant of Stanley's chromatic symmetric function
Nicholas A. Loehr, Gregory S. Warrington
Richard Stanley defined the chromatic symmetric function of a graph and asked whether there are non-isomorphic trees and with . We study variants of the…