***************************************************************************** * 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: St000094 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The depth of an ordered tree. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(t): return t.depth() ----------------------------------------------------------------------------- Statistic values: [[]] => 2 [[],[]] => 2 [[[]]] => 3 [[],[],[]] => 2 [[],[[]]] => 3 [[[]],[]] => 3 [[[],[]]] => 3 [[[[]]]] => 4 [[],[],[],[]] => 2 [[],[],[[]]] => 3 [[],[[]],[]] => 3 [[],[[],[]]] => 3 [[],[[[]]]] => 4 [[[]],[],[]] => 3 [[[]],[[]]] => 3 [[[],[]],[]] => 3 [[[[]]],[]] => 4 [[[],[],[]]] => 3 [[[],[[]]]] => 4 [[[[]],[]]] => 4 [[[[],[]]]] => 4 [[[[[]]]]] => 5 [[],[],[],[],[]] => 2 [[],[],[],[[]]] => 3 [[],[],[[]],[]] => 3 [[],[],[[],[]]] => 3 [[],[],[[[]]]] => 4 [[],[[]],[],[]] => 3 [[],[[]],[[]]] => 3 [[],[[],[]],[]] => 3 [[],[[[]]],[]] => 4 [[],[[],[],[]]] => 3 [[],[[],[[]]]] => 4 [[],[[[]],[]]] => 4 [[],[[[],[]]]] => 4 [[],[[[[]]]]] => 5 [[[]],[],[],[]] => 3 [[[]],[],[[]]] => 3 [[[]],[[]],[]] => 3 [[[]],[[],[]]] => 3 [[[]],[[[]]]] => 4 [[[],[]],[],[]] => 3 [[[[]]],[],[]] => 4 [[[],[]],[[]]] => 3 [[[[]]],[[]]] => 4 [[[],[],[]],[]] => 3 [[[],[[]]],[]] => 4 [[[[]],[]],[]] => 4 [[[[],[]]],[]] => 4 [[[[[]]]],[]] => 5 [[[],[],[],[]]] => 3 [[[],[],[[]]]] => 4 [[[],[[]],[]]] => 4 [[[],[[],[]]]] => 4 [[[],[[[]]]]] => 5 [[[[]],[],[]]] => 4 [[[[]],[[]]]] => 4 [[[[],[]],[]]] => 4 [[[[[]]],[]]] => 5 [[[[],[],[]]]] => 4 [[[[],[[]]]]] => 5 [[[[[]],[]]]] => 5 [[[[[],[]]]]] => 5 [[[[[[]]]]]] => 6 [[],[],[],[],[],[]] => 2 [[],[],[],[],[[]]] => 3 [[],[],[],[[]],[]] => 3 [[],[],[],[[],[]]] => 3 [[],[],[],[[[]]]] => 4 [[],[],[[]],[],[]] => 3 [[],[],[[]],[[]]] => 3 [[],[],[[],[]],[]] => 3 [[],[],[[[]]],[]] => 4 [[],[],[[],[],[]]] => 3 [[],[],[[],[[]]]] => 4 [[],[],[[[]],[]]] => 4 [[],[],[[[],[]]]] => 4 [[],[],[[[[]]]]] => 5 [[],[[]],[],[],[]] => 3 [[],[[]],[],[[]]] => 3 [[],[[]],[[]],[]] => 3 [[],[[]],[[],[]]] => 3 [[],[[]],[[[]]]] => 4 [[],[[],[]],[],[]] => 3 [[],[[[]]],[],[]] => 4 [[],[[],[]],[[]]] => 3 [[],[[[]]],[[]]] => 4 [[],[[],[],[]],[]] => 3 [[],[[],[[]]],[]] => 4 [[],[[[]],[]],[]] => 4 [[],[[[],[]]],[]] => 4 [[],[[[[]]]],[]] => 5 [[],[[],[],[],[]]] => 3 [[],[[],[],[[]]]] => 4 [[],[[],[[]],[]]] => 4 [[],[[],[[],[]]]] => 4 [[],[[],[[[]]]]] => 5 [[],[[[]],[],[]]] => 4 [[],[[[]],[[]]]] => 4 [[],[[[],[]],[]]] => 4 [[],[[[[]]],[]]] => 5 [[],[[[],[],[]]]] => 4 [[],[[[],[[]]]]] => 5 [[],[[[[]],[]]]] => 5 [[],[[[[],[]]]]] => 5 [[],[[[[[]]]]]] => 6 [[[]],[],[],[],[]] => 3 [[[]],[],[],[[]]] => 3 [[[]],[],[[]],[]] => 3 [[[]],[],[[],[]]] => 3 [[[]],[],[[[]]]] => 4 [[[]],[[]],[],[]] => 3 [[[]],[[]],[[]]] => 3 [[[]],[[],[]],[]] => 3 [[[]],[[[]]],[]] => 4 [[[]],[[],[],[]]] => 3 [[[]],[[],[[]]]] => 4 [[[]],[[[]],[]]] => 4 [[[]],[[[],[]]]] => 4 [[[]],[[[[]]]]] => 5 [[[],[]],[],[],[]] => 3 [[[[]]],[],[],[]] => 4 [[[],[]],[],[[]]] => 3 [[[[]]],[],[[]]] => 4 [[[],[]],[[]],[]] => 3 [[[[]]],[[]],[]] => 4 [[[],[]],[[],[]]] => 3 [[[],[]],[[[]]]] => 4 [[[[]]],[[],[]]] => 4 [[[[]]],[[[]]]] => 4 [[[],[],[]],[],[]] => 3 [[[],[[]]],[],[]] => 4 [[[[]],[]],[],[]] => 4 [[[[],[]]],[],[]] => 4 [[[[[]]]],[],[]] => 5 [[[],[],[]],[[]]] => 3 [[[],[[]]],[[]]] => 4 [[[[]],[]],[[]]] => 4 [[[[],[]]],[[]]] => 4 [[[[[]]]],[[]]] => 5 [[[],[],[],[]],[]] => 3 [[[],[],[[]]],[]] => 4 [[[],[[]],[]],[]] => 4 [[[],[[],[]]],[]] => 4 [[[],[[[]]]],[]] => 5 [[[[]],[],[]],[]] => 4 [[[[]],[[]]],[]] => 4 [[[[],[]],[]],[]] => 4 [[[[[]]],[]],[]] => 5 [[[[],[],[]]],[]] => 4 [[[[],[[]]]],[]] => 5 [[[[[]],[]]],[]] => 5 [[[[[],[]]]],[]] => 5 [[[[[[]]]]],[]] => 6 [[[],[],[],[],[]]] => 3 [[[],[],[],[[]]]] => 4 [[[],[],[[]],[]]] => 4 [[[],[],[[],[]]]] => 4 [[[],[],[[[]]]]] => 5 [[[],[[]],[],[]]] => 4 [[[],[[]],[[]]]] => 4 [[[],[[],[]],[]]] => 4 [[[],[[[]]],[]]] => 5 [[[],[[],[],[]]]] => 4 [[[],[[],[[]]]]] => 5 [[[],[[[]],[]]]] => 5 [[[],[[[],[]]]]] => 5 [[[],[[[[]]]]]] => 6 [[[[]],[],[],[]]] => 4 [[[[]],[],[[]]]] => 4 [[[[]],[[]],[]]] => 4 [[[[]],[[],[]]]] => 4 [[[[]],[[[]]]]] => 5 [[[[],[]],[],[]]] => 4 [[[[[]]],[],[]]] => 5 [[[[],[]],[[]]]] => 4 [[[[[]]],[[]]]] => 5 [[[[],[],[]],[]]] => 4 [[[[],[[]]],[]]] => 5 [[[[[]],[]],[]]] => 5 [[[[[],[]]],[]]] => 5 [[[[[[]]]],[]]] => 6 [[[[],[],[],[]]]] => 4 [[[[],[],[[]]]]] => 5 [[[[],[[]],[]]]] => 5 [[[[],[[],[]]]]] => 5 [[[[],[[[]]]]]] => 6 [[[[[]],[],[]]]] => 5 [[[[[]],[[]]]]] => 5 [[[[[],[]],[]]]] => 5 [[[[[[]]],[]]]] => 6 [[[[[],[],[]]]]] => 5 [[[[[],[[]]]]]] => 6 [[[[[[]],[]]]]] => 6 [[[[[[],[]]]]]] => 6 [[[[[[[]]]]]]] => 7 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 16:39 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Feb 17, 2015 at 21:18 by Martin Rubey