5 citations · 5 across the 5 of their papers we have counts for
6 papers
Fast factorization in diagram monoids
Matthias Fresacher, Willow Stewart, Daniel Tubbenhauer
We give explicit algorithms that factor elements of the standard diagram monoids into their usual generators. These algorithms generalize sorting from permutations to partial match…
Generalized diagram categories and monoids, and their representations
Matthias Fresacher, Willow Stewart, Daniel Tubbenhauer
Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and a…
Representation gaps of rigid planar diagram monoids
Willow Stewart, Daniel Tubbenhauer
We define non-pivotal analogs of the Temperley-Lieb, Motzkin, and planar rook monoids, and compute bounds for the sizes of their nontrivial simple representations. From this, we as…
Big data comparison of quantum invariants
Daniel Tubbenhauer, Victor Zhang
We apply big data techniques, including exploratory and topological data analysis, to investigate quantum invariants. More precisely, our study explores the Jones polynomial's stru…
Equivariant neural networks and piecewise linear representation theory
Joel Gibson, Daniel Tubbenhauer, Geordie Williamson
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simpl…
Monoidal categories, representation gap and cryptography
Mikhail Khovanov, Maithreya Sitaraman, Daniel Tubbenhauer
The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids (or semigroups) in cryptography. To overcome this issue we p…