Tootfinder

Abstract String Domain Defined with Word Equations as a Reduced Product (Extended Version)
Antonina Nepeivoda, Ilya Afanasyev
https://arxiv.org/abs/2510.11007 https://

Abstract String Domain Defined with Word Equations as a Reduced Product (Extended Version)
We introduce a string-interval abstract domain, where string intervals are characterized by systems of word equations (encoding lower bounds on string values) and word disequalities (encoding upper bounds). Building upon the lattice structure of string intervals, we define an abstract string object as a reduced product on a string property semilattice, determined by length-non-increasing morphisms. We consider several reduction strategies for abstract string objects and show that upon these str…

Extended Weak Order for the Rank 3 Universal Coxeter Group
Grant Barkley, Colin Defant, Patricia Hersh, Jon McCammond, Thomas McConville, David E Speyer
https://arxiv.org/abs/2509.00871

Extended Weak Order for the Rank 3 Universal Coxeter Group
The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by problems in Kazhdan--Lusztig theory, Matthew Dyer introduced the extended weak order, a poset that contains a copy of the weak order as an order ideal, and he conjectured that the extended weak order for any Coxeter group is a lattice. We prove Dyer's conjecture for the rank 3 universal Coxeter group. This is the first …

Beyond wreath and block
Michal Botur, Tomasz Kowalski
https://arxiv.org/abs/2509.11610 https://arxiv.org/pdf/2509.11610

Beyond wreath and block
We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element flip-flop monoid is replaced by the two-element semilattice.