4 papers
Estimating with a Coin
Jim Propp
We describe a simple Monte Carlo method for estimating by tossing a coin. Although the underlying Catalan-number series identities appear implicitly in the probability theory…
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…
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…
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…