***************************************************************************** * 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: St000085 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The number of linear extensions of the tree. We use Knuth's hook length formula for trees [pg.70, 1]. For an ordered tree $T$ on $n$ vertices, the number of linear extensions is $$ \frac{n!}{\prod_{v\in T}|T_v|}, $$ where $T_v$ is the number of vertices of the subtree rooted at $v$. ----------------------------------------------------------------------------- References: [1] Knuth, D. E. The art of computer programming. Volume 3 [[MathSciNet:0445948]] ----------------------------------------------------------------------------- Code: def tree_hook_product(tree): hook_products = [tree_hook_product(t) for t in tree] return prod(hook_products)*tree.node_number() def tree_hook_formula(tree): return factorial(tree.node_number())/tree_hook_product(tree) def statistic(t): return tree_hook_formula(t) ----------------------------------------------------------------------------- Statistic values: [[]] => 1 [[],[]] => 2 [[[]]] => 1 [[],[],[]] => 6 [[],[[]]] => 3 [[[]],[]] => 3 [[[],[]]] => 2 [[[[]]]] => 1 [[],[],[],[]] => 24 [[],[],[[]]] => 12 [[],[[]],[]] => 12 [[],[[],[]]] => 8 [[],[[[]]]] => 4 [[[]],[],[]] => 12 [[[]],[[]]] => 6 [[[],[]],[]] => 8 [[[[]]],[]] => 4 [[[],[],[]]] => 6 [[[],[[]]]] => 3 [[[[]],[]]] => 3 [[[[],[]]]] => 2 [[[[[]]]]] => 1 [[],[],[],[],[]] => 120 [[],[],[],[[]]] => 60 [[],[],[[]],[]] => 60 [[],[],[[],[]]] => 40 [[],[],[[[]]]] => 20 [[],[[]],[],[]] => 60 [[],[[]],[[]]] => 30 [[],[[],[]],[]] => 40 [[],[[[]]],[]] => 20 [[],[[],[],[]]] => 30 [[],[[],[[]]]] => 15 [[],[[[]],[]]] => 15 [[],[[[],[]]]] => 10 [[],[[[[]]]]] => 5 [[[]],[],[],[]] => 60 [[[]],[],[[]]] => 30 [[[]],[[]],[]] => 30 [[[]],[[],[]]] => 20 [[[]],[[[]]]] => 10 [[[],[]],[],[]] => 40 [[[[]]],[],[]] => 20 [[[],[]],[[]]] => 20 [[[[]]],[[]]] => 10 [[[],[],[]],[]] => 30 [[[],[[]]],[]] => 15 [[[[]],[]],[]] => 15 [[[[],[]]],[]] => 10 [[[[[]]]],[]] => 5 [[[],[],[],[]]] => 24 [[[],[],[[]]]] => 12 [[[],[[]],[]]] => 12 [[[],[[],[]]]] => 8 [[[],[[[]]]]] => 4 [[[[]],[],[]]] => 12 [[[[]],[[]]]] => 6 [[[[],[]],[]]] => 8 [[[[[]]],[]]] => 4 [[[[],[],[]]]] => 6 [[[[],[[]]]]] => 3 [[[[[]],[]]]] => 3 [[[[[],[]]]]] => 2 [[[[[[]]]]]] => 1 [[],[],[],[],[],[]] => 720 [[],[],[],[],[[]]] => 360 [[],[],[],[[]],[]] => 360 [[],[],[],[[],[]]] => 240 [[],[],[],[[[]]]] => 120 [[],[],[[]],[],[]] => 360 [[],[],[[]],[[]]] => 180 [[],[],[[],[]],[]] => 240 [[],[],[[[]]],[]] => 120 [[],[],[[],[],[]]] => 180 [[],[],[[],[[]]]] => 90 [[],[],[[[]],[]]] => 90 [[],[],[[[],[]]]] => 60 [[],[],[[[[]]]]] => 30 [[],[[]],[],[],[]] => 360 [[],[[]],[],[[]]] => 180 [[],[[]],[[]],[]] => 180 [[],[[]],[[],[]]] => 120 [[],[[]],[[[]]]] => 60 [[],[[],[]],[],[]] => 240 [[],[[[]]],[],[]] => 120 [[],[[],[]],[[]]] => 120 [[],[[[]]],[[]]] => 60 [[],[[],[],[]],[]] => 180 [[],[[],[[]]],[]] => 90 [[],[[[]],[]],[]] => 90 [[],[[[],[]]],[]] => 60 [[],[[[[]]]],[]] => 30 [[],[[],[],[],[]]] => 144 [[],[[],[],[[]]]] => 72 [[],[[],[[]],[]]] => 72 [[],[[],[[],[]]]] => 48 [[],[[],[[[]]]]] => 24 [[],[[[]],[],[]]] => 72 [[],[[[]],[[]]]] => 36 [[],[[[],[]],[]]] => 48 [[],[[[[]]],[]]] => 24 [[],[[[],[],[]]]] => 36 [[],[[[],[[]]]]] => 18 [[],[[[[]],[]]]] => 18 [[],[[[[],[]]]]] => 12 [[],[[[[[]]]]]] => 6 [[[]],[],[],[],[]] => 360 [[[]],[],[],[[]]] => 180 [[[]],[],[[]],[]] => 180 [[[]],[],[[],[]]] => 120 [[[]],[],[[[]]]] => 60 [[[]],[[]],[],[]] => 180 [[[]],[[]],[[]]] => 90 [[[]],[[],[]],[]] => 120 [[[]],[[[]]],[]] => 60 [[[]],[[],[],[]]] => 90 [[[]],[[],[[]]]] => 45 [[[]],[[[]],[]]] => 45 [[[]],[[[],[]]]] => 30 [[[]],[[[[]]]]] => 15 [[[],[]],[],[],[]] => 240 [[[[]]],[],[],[]] => 120 [[[],[]],[],[[]]] => 120 [[[[]]],[],[[]]] => 60 [[[],[]],[[]],[]] => 120 [[[[]]],[[]],[]] => 60 [[[],[]],[[],[]]] => 80 [[[],[]],[[[]]]] => 40 [[[[]]],[[],[]]] => 40 [[[[]]],[[[]]]] => 20 [[[],[],[]],[],[]] => 180 [[[],[[]]],[],[]] => 90 [[[[]],[]],[],[]] => 90 [[[[],[]]],[],[]] => 60 [[[[[]]]],[],[]] => 30 [[[],[],[]],[[]]] => 90 [[[],[[]]],[[]]] => 45 [[[[]],[]],[[]]] => 45 [[[[],[]]],[[]]] => 30 [[[[[]]]],[[]]] => 15 [[[],[],[],[]],[]] => 144 [[[],[],[[]]],[]] => 72 [[[],[[]],[]],[]] => 72 [[[],[[],[]]],[]] => 48 [[[],[[[]]]],[]] => 24 [[[[]],[],[]],[]] => 72 [[[[]],[[]]],[]] => 36 [[[[],[]],[]],[]] => 48 [[[[[]]],[]],[]] => 24 [[[[],[],[]]],[]] => 36 [[[[],[[]]]],[]] => 18 [[[[[]],[]]],[]] => 18 [[[[[],[]]]],[]] => 12 [[[[[[]]]]],[]] => 6 [[[],[],[],[],[]]] => 120 [[[],[],[],[[]]]] => 60 [[[],[],[[]],[]]] => 60 [[[],[],[[],[]]]] => 40 [[[],[],[[[]]]]] => 20 [[[],[[]],[],[]]] => 60 [[[],[[]],[[]]]] => 30 [[[],[[],[]],[]]] => 40 [[[],[[[]]],[]]] => 20 [[[],[[],[],[]]]] => 30 [[[],[[],[[]]]]] => 15 [[[],[[[]],[]]]] => 15 [[[],[[[],[]]]]] => 10 [[[],[[[[]]]]]] => 5 [[[[]],[],[],[]]] => 60 [[[[]],[],[[]]]] => 30 [[[[]],[[]],[]]] => 30 [[[[]],[[],[]]]] => 20 [[[[]],[[[]]]]] => 10 [[[[],[]],[],[]]] => 40 [[[[[]]],[],[]]] => 20 [[[[],[]],[[]]]] => 20 [[[[[]]],[[]]]] => 10 [[[[],[],[]],[]]] => 30 [[[[],[[]]],[]]] => 15 [[[[[]],[]],[]]] => 15 [[[[[],[]]],[]]] => 10 [[[[[[]]]],[]]] => 5 [[[[],[],[],[]]]] => 24 [[[[],[],[[]]]]] => 12 [[[[],[[]],[]]]] => 12 [[[[],[[],[]]]]] => 8 [[[[],[[[]]]]]] => 4 [[[[[]],[],[]]]] => 12 [[[[[]],[[]]]]] => 6 [[[[[],[]],[]]]] => 8 [[[[[[]]],[]]]] => 4 [[[[[],[],[]]]]] => 6 [[[[[],[[]]]]]] => 3 [[[[[[]],[]]]]] => 3 [[[[[[],[]]]]]] => 2 [[[[[[[]]]]]]] => 1 [[],[[],[[[[]]]]]] => 35 [[],[[[[[]]]],[]]] => 35 [[],[[[],[[],[]]]]] => 56 [[],[[[],[[[]]]]]] => 28 [[],[[[[]],[[]]]]] => 42 [[],[[[[],[]],[]]]] => 56 [[],[[[[[]]],[]]]] => 28 [[],[[[[],[],[]]]]] => 42 [[],[[[[],[[]]]]]] => 21 [[],[[[[[]],[]]]]] => 21 [[],[[[[[],[]]]]]] => 14 [[],[[[[[[]]]]]]] => 7 [[[]],[[[[[]]]]]] => 21 [[[[[[]]]]],[[]]] => 21 [[[],[[[[]]]]],[]] => 35 [[[[[[]]]],[]],[]] => 35 [[[[],[[],[]]]],[]] => 56 [[[[],[[[]]]]],[]] => 28 [[[[[]],[[]]]],[]] => 42 [[[[[],[]],[]]],[]] => 56 [[[[[[]]],[]]],[]] => 28 [[[[[],[],[]]]],[]] => 42 [[[[[],[[]]]]],[]] => 21 [[[[[[]],[]]]],[]] => 21 [[[[[[],[]]]]],[]] => 14 [[[[[[[]]]]]],[]] => 7 [[],[[],[[],[[],[]]]]] => 384 [[],[[],[[[],[]],[]]]] => 384 [[],[[[],[]],[[],[]]]] => 640 [[],[[[],[[],[]]],[]]] => 384 [[],[[[[],[]],[]],[]]] => 384 [[],[[[[],[[[]]]]]]] => 32 [[],[[[[[[]]],[]]]]] => 32 [[],[[[[[],[],[]]]]]] => 48 [[],[[[[[],[[]]]]]]] => 24 [[],[[[[[[]],[]]]]]] => 24 [[],[[[[[[],[]]]]]]] => 16 [[],[[[[[[[]]]]]]]] => 8 [[[],[]],[[],[[],[]]]] => 896 [[[],[]],[[[],[]],[]]] => 896 [[[],[[],[]]],[[],[]]] => 896 [[[[],[]],[]],[[],[]]] => 896 [[[],[[],[[],[]]]],[]] => 384 [[[],[[[],[]],[]]],[]] => 384 [[[[],[]],[[],[]]],[]] => 640 [[[[],[[],[]]],[]],[]] => 384 [[[[[],[]],[]],[]],[]] => 384 [[[[[],[[[]]]]]],[]] => 32 [[[[[[[]]],[]]]],[]] => 32 [[[[[[],[],[]]]]],[]] => 48 [[[[[[],[[]]]]]],[]] => 24 [[[[[[[]],[]]]]],[]] => 24 [[[[[[[],[]]]]]],[]] => 16 [[[[[[[[]]]]]]],[]] => 8 [[[[[[[[[]]]]]]]],[]] => 9 [[],[[[[[[[[]]]]]]]]] => 9 [[[[[[[[],[]]]]]]],[]] => 18 [[],[[[[[[[],[]]]]]]]] => 18 [[[[[[[[]],[]]]]]],[]] => 27 [[[[[[[],[[]]]]]]],[]] => 27 [[],[[[[[[[]],[]]]]]]] => 27 [[],[[[[[[],[[]]]]]]]] => 27 [[],[[],[[],[[],[[],[]]]]]] => 3840 [[],[[],[[],[[[],[]],[]]]]] => 3840 [[],[[],[[[],[]],[[],[]]]]] => 6400 [[],[[],[[[],[[],[]]],[]]]] => 3840 [[],[[],[[[[],[]],[]],[]]]] => 3840 [[],[[[],[]],[[],[[],[]]]]] => 8960 [[],[[[],[]],[[[],[]],[]]]] => 8960 [[],[[[],[[],[]]],[[],[]]]] => 8960 [[],[[[[],[]],[]],[[],[]]]] => 8960 [[],[[[],[[],[[],[]]]],[]]] => 3840 [[],[[[],[[[],[]],[]]],[]]] => 3840 [[],[[[[],[]],[[],[]]],[]]] => 6400 [[],[[[[],[[],[]]],[]],[]]] => 3840 [[],[[[[[],[]],[]],[]],[]]] => 3840 [[[],[]],[[],[[],[[],[]]]]] => 11520 [[[],[]],[[],[[[],[]],[]]]] => 11520 [[[],[]],[[[],[]],[[],[]]]] => 19200 [[[],[]],[[[],[[],[]]],[]]] => 11520 [[[],[]],[[[[],[]],[]],[]]] => 11520 [[[],[[],[]]],[[],[[],[]]]] => 16128 [[[],[[],[]]],[[[],[]],[]]] => 16128 [[[[],[]],[]],[[],[[],[]]]] => 16128 [[[[],[]],[]],[[[],[]],[]]] => 16128 [[[],[[],[[],[]]]],[[],[]]] => 11520 [[[],[[[],[]],[]]],[[],[]]] => 11520 [[[[],[]],[[],[]]],[[],[]]] => 19200 [[[[],[[],[]]],[]],[[],[]]] => 11520 [[[[[],[]],[]],[]],[[],[]]] => 11520 [[[],[[],[[],[[],[]]]]],[]] => 3840 [[[],[[],[[[],[]],[]]]],[]] => 3840 [[[],[[[],[]],[[],[]]]],[]] => 6400 [[[],[[[],[[],[]]],[]]],[]] => 3840 [[[],[[[[],[]],[]],[]]],[]] => 3840 [[[[],[]],[[],[[],[]]]],[]] => 8960 [[[[],[]],[[[],[]],[]]],[]] => 8960 [[[[],[[],[]]],[[],[]]],[]] => 8960 [[[[[],[]],[]],[[],[]]],[]] => 8960 [[[[],[[],[[],[]]]],[]],[]] => 3840 [[[[],[[[],[]],[]]],[]],[]] => 3840 [[[[[],[]],[[],[]]],[]],[]] => 6400 [[[[[],[[],[]]],[]],[]],[]] => 3840 [[[[[[],[]],[]],[]],[]],[]] => 3840 [[[[[[[[[[]]]]]]]]],[]] => 10 [[],[[[[[[[[[]]]]]]]]]] => 10 [[[[[[[[[],[]]]]]]]],[]] => 20 [[],[[[[[[[[],[]]]]]]]]] => 20 [[[[[[[[[[[]]]]]]]]]],[]] => 11 [[],[[[[[[[[[[]]]]]]]]]]] => 11 [[],[[],[[],[[],[[],[[],[]]]]]]] => 46080 [[],[[],[[],[[],[[[],[]],[]]]]]] => 46080 [[],[[],[[],[[[],[]],[[],[]]]]]] => 76800 [[],[[],[[],[[[],[[],[]]],[]]]]] => 46080 [[],[[],[[],[[[[],[]],[]],[]]]]] => 46080 [[],[[],[[[],[]],[[],[[],[]]]]]] => 107520 [[],[[],[[[],[]],[[[],[]],[]]]]] => 107520 [[],[[],[[[],[[],[]]],[[],[]]]]] => 107520 [[],[[],[[[[],[]],[]],[[],[]]]]] => 107520 [[],[[],[[[],[[],[[],[]]]],[]]]] => 46080 [[],[[],[[[],[[[],[]],[]]],[]]]] => 46080 [[],[[],[[[[],[]],[[],[]]],[]]]] => 76800 [[],[[],[[[[],[[],[]]],[]],[]]]] => 46080 [[],[[],[[[[[],[]],[]],[]],[]]]] => 46080 [[],[[[],[]],[[],[[],[[],[]]]]]] => 138240 [[],[[[],[]],[[],[[[],[]],[]]]]] => 138240 [[],[[[],[]],[[[],[]],[[],[]]]]] => 230400 [[],[[[],[]],[[[],[[],[]]],[]]]] => 138240 [[],[[[],[]],[[[[],[]],[]],[]]]] => 138240 [[],[[[],[[],[]]],[[],[[],[]]]]] => 193536 [[],[[[],[[],[]]],[[[],[]],[]]]] => 193536 [[],[[[[],[]],[]],[[],[[],[]]]]] => 193536 [[],[[[[],[]],[]],[[[],[]],[]]]] => 193536 [[],[[[],[[],[[],[]]]],[[],[]]]] => 138240 [[],[[[],[[[],[]],[]]],[[],[]]]] => 138240 [[],[[[[],[]],[[],[]]],[[],[]]]] => 230400 [[],[[[[],[[],[]]],[]],[[],[]]]] => 138240 [[],[[[[[],[]],[]],[]],[[],[]]]] => 138240 [[],[[[],[[],[[],[[],[]]]]],[]]] => 46080 [[],[[[],[[],[[[],[]],[]]]],[]]] => 46080 [[],[[[],[[[],[]],[[],[]]]],[]]] => 76800 [[],[[[],[[[],[[],[]]],[]]],[]]] => 46080 [[],[[[],[[[[],[]],[]],[]]],[]]] => 46080 [[],[[[[],[]],[[],[[],[]]]],[]]] => 107520 [[],[[[[],[]],[[[],[]],[]]],[]]] => 107520 [[],[[[[],[[],[]]],[[],[]]],[]]] => 107520 [[],[[[[[],[]],[]],[[],[]]],[]]] => 107520 [[],[[[[],[[],[[],[]]]],[]],[]]] => 46080 [[],[[[[],[[[],[]],[]]],[]],[]]] => 46080 [[],[[[[[],[]],[[],[]]],[]],[]]] => 76800 [[],[[[[[],[[],[]]],[]],[]],[]]] => 46080 [[],[[[[[[],[]],[]],[]],[]],[]]] => 46080 [[[],[]],[[],[[],[[],[[],[]]]]]] => 168960 [[[],[]],[[],[[],[[[],[]],[]]]]] => 168960 [[[],[]],[[],[[[],[]],[[],[]]]]] => 281600 [[[],[]],[[],[[[],[[],[]]],[]]]] => 168960 [[[],[]],[[],[[[[],[]],[]],[]]]] => 168960 [[[],[]],[[[],[]],[[],[[],[]]]]] => 394240 [[[],[]],[[[],[]],[[[],[]],[]]]] => 394240 [[[],[]],[[[],[[],[]]],[[],[]]]] => 394240 [[[],[]],[[[[],[]],[]],[[],[]]]] => 394240 [[[],[]],[[[],[[],[[],[]]]],[]]] => 168960 [[[],[]],[[[],[[[],[]],[]]],[]]] => 168960 [[[],[]],[[[[],[]],[[],[]]],[]]] => 281600 [[[],[]],[[[[],[[],[]]],[]],[]]] => 168960 [[[],[]],[[[[[],[]],[]],[]],[]]] => 168960 [[[],[[],[]]],[[],[[],[[],[]]]]] => 304128 [[[],[[],[]]],[[],[[[],[]],[]]]] => 304128 [[[],[[],[]]],[[[],[]],[[],[]]]] => 506880 [[[],[[],[]]],[[[],[[],[]]],[]]] => 304128 [[[],[[],[]]],[[[[],[]],[]],[]]] => 304128 [[[[],[]],[]],[[],[[],[[],[]]]]] => 304128 [[[[],[]],[]],[[],[[[],[]],[]]]] => 304128 [[[[],[]],[]],[[[],[]],[[],[]]]] => 506880 [[[[],[]],[]],[[[],[[],[]]],[]]] => 304128 [[[[],[]],[]],[[[[],[]],[]],[]]] => 304128 [[[],[[],[[],[]]]],[[],[[],[]]]] => 304128 [[[],[[],[[],[]]]],[[[],[]],[]]] => 304128 [[[],[[[],[]],[]]],[[],[[],[]]]] => 304128 [[[],[[[],[]],[]]],[[[],[]],[]]] => 304128 [[[[],[]],[[],[]]],[[],[[],[]]]] => 506880 [[[[],[]],[[],[]]],[[[],[]],[]]] => 506880 [[[[],[[],[]]],[]],[[],[[],[]]]] => 304128 [[[[],[[],[]]],[]],[[[],[]],[]]] => 304128 [[[[[],[]],[]],[]],[[],[[],[]]]] => 304128 [[[[[],[]],[]],[]],[[[],[]],[]]] => 304128 [[[],[[],[[],[[],[]]]]],[[],[]]] => 168960 [[[],[[],[[[],[]],[]]]],[[],[]]] => 168960 [[[],[[[],[]],[[],[]]]],[[],[]]] => 281600 [[[],[[[],[[],[]]],[]]],[[],[]]] => 168960 [[[],[[[[],[]],[]],[]]],[[],[]]] => 168960 [[[[],[]],[[],[[],[]]]],[[],[]]] => 394240 [[[[],[]],[[[],[]],[]]],[[],[]]] => 394240 [[[[],[[],[]]],[[],[]]],[[],[]]] => 394240 [[[[[],[]],[]],[[],[]]],[[],[]]] => 394240 [[[[],[[],[[],[]]]],[]],[[],[]]] => 168960 [[[[],[[[],[]],[]]],[]],[[],[]]] => 168960 [[[[[],[]],[[],[]]],[]],[[],[]]] => 281600 [[[[[],[[],[]]],[]],[]],[[],[]]] => 168960 [[[[[[],[]],[]],[]],[]],[[],[]]] => 168960 [[[],[[],[[],[[],[[],[]]]]]],[]] => 46080 [[[],[[],[[],[[[],[]],[]]]]],[]] => 46080 [[[],[[],[[[],[]],[[],[]]]]],[]] => 76800 [[[],[[],[[[],[[],[]]],[]]]],[]] => 46080 [[[],[[],[[[[],[]],[]],[]]]],[]] => 46080 [[[],[[[],[]],[[],[[],[]]]]],[]] => 107520 [[[],[[[],[]],[[[],[]],[]]]],[]] => 107520 [[[],[[[],[[],[]]],[[],[]]]],[]] => 107520 [[[],[[[[],[]],[]],[[],[]]]],[]] => 107520 [[[],[[[],[[],[[],[]]]],[]]],[]] => 46080 [[[],[[[],[[[],[]],[]]],[]]],[]] => 46080 [[[],[[[[],[]],[[],[]]],[]]],[]] => 76800 [[[],[[[[],[[],[]]],[]],[]]],[]] => 46080 [[[],[[[[[],[]],[]],[]],[]]],[]] => 46080 [[[[],[]],[[],[[],[[],[]]]]],[]] => 138240 [[[[],[]],[[],[[[],[]],[]]]],[]] => 138240 [[[[],[]],[[[],[]],[[],[]]]],[]] => 230400 [[[[],[]],[[[],[[],[]]],[]]],[]] => 138240 [[[[],[]],[[[[],[]],[]],[]]],[]] => 138240 [[[[],[[],[]]],[[],[[],[]]]],[]] => 193536 [[[[],[[],[]]],[[[],[]],[]]],[]] => 193536 [[[[[],[]],[]],[[],[[],[]]]],[]] => 193536 [[[[[],[]],[]],[[[],[]],[]]],[]] => 193536 [[[[],[[],[[],[]]]],[[],[]]],[]] => 138240 [[[[],[[[],[]],[]]],[[],[]]],[]] => 138240 [[[[[],[]],[[],[]]],[[],[]]],[]] => 230400 [[[[[],[[],[]]],[]],[[],[]]],[]] => 138240 [[[[[[],[]],[]],[]],[[],[]]],[]] => 138240 [[[[],[[],[[],[[],[]]]]],[]],[]] => 46080 [[[[],[[],[[[],[]],[]]]],[]],[]] => 46080 [[[[],[[[],[]],[[],[]]]],[]],[]] => 76800 [[[[],[[[],[[],[]]],[]]],[]],[]] => 46080 [[[[],[[[[],[]],[]],[]]],[]],[]] => 46080 [[[[[],[]],[[],[[],[]]]],[]],[]] => 107520 [[[[[],[]],[[[],[]],[]]],[]],[]] => 107520 [[[[[],[[],[]]],[[],[]]],[]],[]] => 107520 [[[[[[],[]],[]],[[],[]]],[]],[]] => 107520 [[[[[],[[],[[],[]]]],[]],[]],[]] => 46080 [[[[[],[[[],[]],[]]],[]],[]],[]] => 46080 [[[[[[],[]],[[],[]]],[]],[]],[]] => 76800 [[[[[[],[[],[]]],[]],[]],[]],[]] => 46080 [[[[[[[],[]],[]],[]],[]],[]],[]] => 46080 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 10:24 by Viviane Pons ----------------------------------------------------------------------------- Last Updated: Mar 20, 2019 at 00:53 by Martin Rubey