2024/08/01 by Samuel Kutin, Kutin, Samuel A., Lawren Smithline +1 · 1 citation
Computer Science · Mathematics · #05A05 #Combinatorics (math.CO) #FOS: Mathematics #Machine Learning and Algorithms #Mathematical Approximation and Integration #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2408.00903
openalex publication_date 2024/08/01 · openalex created_date 2024/10/24 · openalex updated_date 2026/07/28
We introduce a guessing game, permutation Wordle, in which a guesser attempts to recover a hidden permutation in Sn. In each round, the guesser guesses a permutation (using information from previous rounds) and is told which entries of that permutation are correct. We describe a natural guessing strategy, which we believe to be optimal. We show that the number of permutations this strategy solves in k+1 rounds is the Eulerian number A(n,k). We also describe an extension to suited permutations: the setter chooses a permutation in Sn and also a coloring of [n] using s colors. We generalize our strategy, give a recurrence for the number of suited permutations solved in k+1 rounds, and relate these numbers to the Eulerian numbers. In the case of two suits, or signed permutations, we also relate these numbers to the Eulerian numbers of type B.