Solving Combinatorial Counting Problems with Weighted First-Order Model Counting

arXiv:2605.24845v1 Announce Type: new Abstract: Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic constraints, solving it remains a stubbornly manual exercise. Closed-form derivations are powerful but brittle, while naive encodings to propositional model counting or constraint satisfaction destroy the exchangeability th