16 citations · 62 across the 23 of their papers we have counts for
18 papers · 1 filter
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…
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…
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…
Abacus-histories and the combinatorics of creation operators
Nicholas A. Loehr, Gregory S. Warrington
Creation operators act on symmetric functions to build Schur functions, Hall--Littlewood polynomials, and related symmetric functions one row at a time. Haglund, Morse, Zabrocki, a…
Orthogonal bases for transportation polytopes applied to Latin squares, magic squares and Sudoku boards
Gregory S. Warrington
We give a simple construction of an orthogonal basis for the space of m by n matrices with row and column sums equal to zero. This vector space corresponds to the affine space natu…
Sweep maps: A continuous family of sorting algorithms
Drew Armstrong, Nicholas A. Loehr, Gregory S. Warrington
We define a family of maps on lattice paths, called sweep maps, that assign levels to each step in the path and sort steps according to their level. Surprisingly, although sweep ma…