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Intersection statistics for antichains in minuscule posets
James Propp
For a finite poset , we study the expected size of the intersection of two independent uniformly random antichains. Equivalently, we evaluate the sum of over all or…
Grid designs
Alon Danai, Joshua Kou, Andy Latto +2
We define a grid graph as a Cartesian product of path-graphs or cycle-graphs as shown in Figure 1, and we ask, when can the edge set of a complete graph be expresse…
Hyperbinary partitions and q-deformed rationals
Thomas McConville, James Propp, Bruce E. Sagan
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of 2 and every part appears at most twice. We give three applications of the length…
Counting Triangles in Triangles
Jim Propp, Adam Propp-Gubin
We give a formula for counting the triangles in a picture consisting of the three sides of a triangle and some cevians. This lets us prove statements that are claimed without proof…
Tilings of Benzels via Generalized Compression
Colin Defant, Leigh Foster, Rupert Li +2
Defant, Li, Propp, and Young recently resolved two enumerative conjectures of Propp concerning the tilings of regions in the hexagonal grid called benzels using two types of protot…