***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001763 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The Hurwitz number of an integer partition. See [eq.(9),pg.21, 1]. ----------------------------------------------------------------------------- References: [1] Hurwitz, A. Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten [[MathSciNet:1510692]] ----------------------------------------------------------------------------- Code: def statistic(la): n = sum(la) c = len(la) return factorial(n + c - 2) * n^(c - 3) * prod(p^p / factorial(p - 1) for p in la) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 3 [2,1] => 8 [1,1,1] => 24 [4] => 16 [3,1] => 81 [2,2] => 96 [2,1,1] => 480 [1,1,1,1] => 2880 [5] => 125 [4,1] => 1024 [3,2] => 1296 [3,1,1] => 9720 [2,2,1] => 11520 [2,1,1,1] => 100800 [1,1,1,1,1] => 1008000 [6] => 1296 [5,1] => 15625 [4,2] => 20480 [4,1,1] => 215040 [3,3] => 21870 [3,2,1] => 272160 [3,1,1,1] => 3265920 [2,2,2] => 322560 [2,2,1,1] => 3870720 [2,1,1,1,1] => 52254720 [1,1,1,1,1,1] => 783820800 [7] => 16807 [6,1] => 279936 [5,2] => 375000 [5,1,1] => 5250000 [4,3] => 414720 [4,2,1] => 6881280 [4,1,1,1] => 108380160 [3,3,1] => 7348320 [3,2,2] => 8709120 [3,2,1,1] => 137168640 [2,2,2,1] => 162570240 [8] => 262144 [7,1] => 5764801 [6,2] => 7838208 [6,1,1] => 141087744 [5,3] => 8859375 [5,2,1] => 189000000 [4,4] => 9175040 [4,3,1] => 209018880 [4,2,2] => 247726080 [3,3,2] => 264539520 [9] => 4782969 [8,1] => 134217728 [7,2] => 184473632 [6,3] => 211631616 [5,4] => 224000000 [10] => 100000000 ----------------------------------------------------------------------------- Created: Jan 11, 2022 at 18:45 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 28, 2023 at 00:15 by Martin Rubey