11 citations · 33 across the 13 of their papers we have counts for
17 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…
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 =…
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…
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…
Foatic actions of the symmetric group and fixed-point homomesy
Michael LaCroix, Tom Roby
We study maps on the set of permutations of n generated by the Rényi-Foata map intertwined with other dihedral symmetries (of a permutation considered as a 0-1 matrix). Iterating t…