4 papers
AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
Eugenio Cainelli, Lorenzo Luccioli, Alessandro Iraci +1
We introduce Bench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficie…
Mapping Uncharted Symmetries: Machine Discovery in Combinatorics
Eugenio Cainelli, Lorenzo Luccioli, Alessandro Iraci +2
Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In part…
Falling stars: a fall-decorated rational shuffle theorem
Alessandro Iraci, Roberto Pagaria, Giovanni Paolini
In this paper, we formulate a rational analog of the fall Delta theorem and the Delta square conjecture. We find a new dinv statistic on fall-decorated paths on a $(m+k) \times (n+…
Learning to Play 7 Wonders Duel Without Human Supervision
Giovanni Paolini, Lorenzo Moreschini, Francesco Veneziano +1
This paper introduces ZeusAI, an artificial intelligence system developed to play the board game 7 Wonders Duel. Inspired by the AlphaZero reinforcement learning algorithm, ZeusAI…