4 citations · 11 across the 7 of their papers we have counts for
8 papers
Parity Property of Hexagonal Sliding Puzzles
Ray Karpman, Erika Roldan
We study the puzzle graphs of hexagonal sliding puzzles of various shapes and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvabilit…
Isotopy graphs of Latin tableaux
R. Karpman, É. Roldán
Latin tableaux are a generalization of Latin squares, which first appeared in the early 2000's in a paper of Chow, Fan, Goemans, and Vondrák. Here, we extend the notion of isotopy,…
The Purity Conjecture in Type
Rachel Karpman
A collection of -element subsets of is weakly separated if for each , when the integers are arranged around…
Triangulations and soliton graphs for totally positive Grassmannian
Rachel Karpman, Yuji Kodama
The KP equation is a nonlinear dispersive wave equation which provides an excellent model for resonant interactions of shallow-water waves. It is well known that regular soliton so…
Total positivity for the Lagrangian Grassmannian
Rachel Karpman
The stratification of the Grassmannian by positroid varieties has been the subject of extensive research. Positroid varieties are in bijection with a number of combinatorial object…
Combinatorics of symmetric plabic graphs
Rachel Karpman, Yi Su
A plabic graph is a planar bicolored graph embedded in a disk, which satisfies some combinatorial conditions. Postnikov's boundary measurement map takes the space of positive edge…