4 papers
A Census of New Snake-in-the-Box Records
Paul Orland, Lucas Fagan, Michele Tarquini +7
The snake-in-the-box problem, introduced by Kautz in 1958, asks for the longest induced (chordless) path, called a snake, in the hypercube graph . The maximum length is…
fkcompute: an efficient invariant calculator
Paul Orland, Davide Passaro, Lara San Martín Suárez +2
We introduce fkcompute, an open-source package for computing the Gukov--Manolescu invariant of links from a braid presentation. fkcompute implements Park's inverted state sum throu…
Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra
Giorgi Butbaia, Paul Orland, Coco Huang +7
Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative exam…
Quantum Invariants and Fiberedness
Paul Orland, Lara San Martín Suárez, Toby Saunders-A'Court +1
We explore the topological significance of the Gukov-Manolescu knot series . We show that the leading coefficient of is a monomial and express its exponent in terms of t…