6 papers
Detropicalization as a proof technique
Darij Grinberg, Tom Roby
Rational functions make sense over any commutative ring, as long as the denominators are invertible. When there is no subtraction involved, they even apply over semirings (rings wi…
Iterative properties of birational rowmotion
Darij Grinberg, Tom Roby
We study a birational map associated to any finite poset P. This map is a far-reaching generalization (found by Einstein and Propp) of classical rowmotion, which is a certain permu…
Whirling injections, surjections, and other functions between finite sets
Michael Joseph, James Propp, Tom Roby
This paper analyzes a certain action called "whirling" that can be defined on any family of functions between two finite sets equipped with a linear (or cyclic) ordering. Many maps…
Rowmotion on the chain of V's poset and whirling dynamics
Matthew Plante, Tom Roby
Given a finite poset , we study the _whirling_ action on vertex-labelings of with the elements . When such labelings are (weakly) order-reversing, we ca…
Rowmotion on fences
Sergi Elizalde, Matthew Plante, Tom Roby +1
A fence is a poset with elements F = {x_1, x_2, ..., x_n} and covers x_1 < x_2 < ... < x_a > x_{a+1} > ... > x_b < x_{b+1} < ... where a, b, ... are positive integers. We investiga…
Monomial identities in the Weyl algebra
Darij Grinberg, Tom Roby, Stephan Wagner +1
Motivated by a question and some enumerative conjectures of Richard Stanley, we explore the equivalence classes of words in the Weyl algebra, $\mathbf{k} \left< D,U \mid DU - UD =…