344 citations · 1.5k across the 52 of their papers we have counts for
57 papers
Dimers, filters, and -deformed real numbers
James Propp
This article associates to each positive real number a dimer model on a snake graph with activity parameter whose structure is determined by the continued fraction expans…
Tilings of Benzels via the Abacus Bijection
Colin Defant, Rupert Li, James Propp +1
Propp recently introduced regions in the hexagonal grid called benzels and stated several enumerative conjectures about the tilings of benzels using two types of prototiles called…
Trimer covers in the triangular grid: twenty mostly open problems
James Propp
In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify s…
A pentagonal number theorem for tribone tilings
Jesse Kim, James Propp
Conway and Lagarias showed that certain roughly triangular regions in the hexagonal grid cannot be tiled by shapes Thurston later dubbed tribones. Here we study a two-parameter fam…
Some 2-adic conjectures concerning polyomino tilings of Aztec diamonds
James Propp
For various sets of tiles, we count the ways to tile an Aztec diamond of order using tiles from that set. The resulting function often has interesting behavior when one…
Homomesy via Toggleability Statistics
Colin Defant, Sam Hopkins, Svetlana Poznanović +1
The rowmotion operator acting on the set of order ideals of a finite poset has been the focus of a significant amount of recent research. One of the major goals has been to exhibit…