7 citations · 17 across the 6 of their papers we have counts for
9 papers
Bosonic Quantum Computational Complexity
Ulysse Chabaud, Michael Joseph, Saeed Mehraban +1
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-d…
Torsors and tilings from toric toggling
Colin Defant, Michael Joseph, Matthew Macauley +1
Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied s…
The birational Lalanne-Kreweras involution
Sam Hopkins, Michael Joseph
The Lalanne-Kreweras involution is an involution on the set of Dyck paths which combinatorially exhibits the symmetry of the number of valleys and major index statistics. We define…
A birational lifting of the Stanley-Thomas word on products of two chains
Michael Joseph, Tom Roby
The dynamics of certain combinatorial actions and their liftings to actions at the piecewise-linear and birational level have been studied lately with an eye towards questions of p…
Birational and noncommutative lifts of antichain toggling and rowmotion
Michael Joseph, Tom Roby
The rowmotion action on order ideals or on antichains of a finite partially ordered set has been studied (under a variety of names) by many authors. Depending on the poset, one fin…
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…
Antichain toggling and rowmotion
Michael Joseph
In this paper, we analyze the toggle group on the set of antichains of a poset. Toggle groups, generated by simple involutions, were first introduced by Cameron and Fon-Der-Flaass…
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…
Noncrossing partitions, toggles, and homomesies
David Einstein, Miriam Farber, Emily Gunawan +4
We introduce natural involutions ("toggles") on the set of noncrossing partitions of size , along with certain composite operations obtained by composing thes…