The permutation ranking algorithm described in the article can be generalized to a so-called multinomial ranking, one of several rankings implemented in Haskell

The permutation ranking algorithm described in the article can be generalized to a so-called multinomial ranking, one of several rankings implemented in Haskell [1]. E.g. > let r = multinomialRanking (zip "abc" [1..3]) > size r 60 > unrank r 42 "cbcabc" > rank r "cbcabc" 42 Various types of rankings, together with combinators to build up more complex ones, were implemented as part of the chess position ranking project [2] which aims to rank a subset of all chess positions that includes all legal ones: > let cpr = sideToMoveRanking `composeURI` (caseRanking `composeRI` wArmyStatRanking `composeURI` bArmyStatRanking `composeRI` guardRanking `composeRI` enPassantRanking `composeURI` epOppRanking `composeURI` sandwichRanking `composeRI` opposeRanking `composeURI` pawnRanking `composeURI` castleRanking `composeURI` wArmyRanking `composeURI` bArmyRanking `composeURI` pieceRanking) $ emptyURPosition > size cpr 8726713169886222032347729969256422370854716254 > writeFEN . toPosition . unrank cpr $ 2389124290426577024216048831051262280148947032 "1r6/1qrRPk2/1rn1Rn1n/1RQRR2R/3P4/3b2BN/1Knn1b1b/1BR5 w - - 0 1" > rank cpr . fromPosition . readFEN $ "1r6/1qrRPk2/1rn1Rn1n/1RQRR2R/3P4/3b2BN/1Knn1b1b/1BR5 w - - 0 1" 2389124290426577024216048831051262280148947032 Position data includes side to move, castling status, and en-passant status. This ranking allows one to sample millions of random such positions, determine how many are legal, and thus obtain an accurate estimate of 4.8 * 10^44 legal chess positions. [1] https://github.com/tromp/ChessPositionRanking/blob/main/src/Data/Ranking.hs https://github.com/tromp/ChessPositionRanking/blob/main/src/... [2] https://github.com/tromp/ChessPositionRanking https://github.com/tromp/ChessPositionRanking