Publications (17)
Toggling independent sets of a path graph
Michael Joseph, Tom Roby
This paper explores the orbit structure and homomesy (constant averages over orbits) properties of certain actions of toggle groups on the collection of independent sets of a path…
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…
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…
Equivalence Classes of Permutations under Various Relations Generated by Constrained Transpositions
Steven Linton, James Propp, Tom Roby +1
We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our mo…
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…
Birational rowmotion on a rectangle over a noncommutative ring
Darij Grinberg, Tom Roby
We extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This r…