***************************************************************************** * 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: St000168 ----------------------------------------------------------------------------- Collection: Ordered trees ----------------------------------------------------------------------------- Description: The number of internal nodes of an ordered tree. A node is internal if it is neither the root nor a leaf. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(t): stack = [c for c in t] ni = 0 while len(stack)!=0: tree = stack.pop() if len(tree)!=0: ni+=1 stack.extend(tree) return ni ----------------------------------------------------------------------------- Statistic values: [[]] => 0 [[],[]] => 0 [[[]]] => 1 [[],[],[]] => 0 [[],[[]]] => 1 [[[]],[]] => 1 [[[],[]]] => 1 [[[[]]]] => 2 [[],[],[],[]] => 0 [[],[],[[]]] => 1 [[],[[]],[]] => 1 [[],[[],[]]] => 1 [[],[[[]]]] => 2 [[[]],[],[]] => 1 [[[]],[[]]] => 2 [[[],[]],[]] => 1 [[[[]]],[]] => 2 [[[],[],[]]] => 1 [[[],[[]]]] => 2 [[[[]],[]]] => 2 [[[[],[]]]] => 2 [[[[[]]]]] => 3 [[],[],[],[],[]] => 0 [[],[],[],[[]]] => 1 [[],[],[[]],[]] => 1 [[],[],[[],[]]] => 1 [[],[],[[[]]]] => 2 [[],[[]],[],[]] => 1 [[],[[]],[[]]] => 2 [[],[[],[]],[]] => 1 [[],[[[]]],[]] => 2 [[],[[],[],[]]] => 1 [[],[[],[[]]]] => 2 [[],[[[]],[]]] => 2 [[],[[[],[]]]] => 2 [[],[[[[]]]]] => 3 [[[]],[],[],[]] => 1 [[[]],[],[[]]] => 2 [[[]],[[]],[]] => 2 [[[]],[[],[]]] => 2 [[[]],[[[]]]] => 3 [[[],[]],[],[]] => 1 [[[[]]],[],[]] => 2 [[[],[]],[[]]] => 2 [[[[]]],[[]]] => 3 [[[],[],[]],[]] => 1 [[[],[[]]],[]] => 2 [[[[]],[]],[]] => 2 [[[[],[]]],[]] => 2 [[[[[]]]],[]] => 3 [[[],[],[],[]]] => 1 [[[],[],[[]]]] => 2 [[[],[[]],[]]] => 2 [[[],[[],[]]]] => 2 [[[],[[[]]]]] => 3 [[[[]],[],[]]] => 2 [[[[]],[[]]]] => 3 [[[[],[]],[]]] => 2 [[[[[]]],[]]] => 3 [[[[],[],[]]]] => 2 [[[[],[[]]]]] => 3 [[[[[]],[]]]] => 3 [[[[[],[]]]]] => 3 [[[[[[]]]]]] => 4 [[],[],[],[],[],[]] => 0 [[],[],[],[],[[]]] => 1 [[],[],[],[[]],[]] => 1 [[],[],[],[[],[]]] => 1 [[],[],[],[[[]]]] => 2 [[],[],[[]],[],[]] => 1 [[],[],[[]],[[]]] => 2 [[],[],[[],[]],[]] => 1 [[],[],[[[]]],[]] => 2 [[],[],[[],[],[]]] => 1 [[],[],[[],[[]]]] => 2 [[],[],[[[]],[]]] => 2 [[],[],[[[],[]]]] => 2 [[],[],[[[[]]]]] => 3 [[],[[]],[],[],[]] => 1 [[],[[]],[],[[]]] => 2 [[],[[]],[[]],[]] => 2 [[],[[]],[[],[]]] => 2 [[],[[]],[[[]]]] => 3 [[],[[],[]],[],[]] => 1 [[],[[[]]],[],[]] => 2 [[],[[],[]],[[]]] => 2 [[],[[[]]],[[]]] => 3 [[],[[],[],[]],[]] => 1 [[],[[],[[]]],[]] => 2 [[],[[[]],[]],[]] => 2 [[],[[[],[]]],[]] => 2 [[],[[[[]]]],[]] => 3 [[],[[],[],[],[]]] => 1 [[],[[],[],[[]]]] => 2 [[],[[],[[]],[]]] => 2 [[],[[],[[],[]]]] => 2 [[],[[],[[[]]]]] => 3 [[],[[[]],[],[]]] => 2 [[],[[[]],[[]]]] => 3 [[],[[[],[]],[]]] => 2 [[],[[[[]]],[]]] => 3 [[],[[[],[],[]]]] => 2 [[],[[[],[[]]]]] => 3 [[],[[[[]],[]]]] => 3 [[],[[[[],[]]]]] => 3 [[],[[[[[]]]]]] => 4 [[[]],[],[],[],[]] => 1 [[[]],[],[],[[]]] => 2 [[[]],[],[[]],[]] => 2 [[[]],[],[[],[]]] => 2 [[[]],[],[[[]]]] => 3 [[[]],[[]],[],[]] => 2 [[[]],[[]],[[]]] => 3 [[[]],[[],[]],[]] => 2 [[[]],[[[]]],[]] => 3 [[[]],[[],[],[]]] => 2 [[[]],[[],[[]]]] => 3 [[[]],[[[]],[]]] => 3 [[[]],[[[],[]]]] => 3 [[[]],[[[[]]]]] => 4 [[[],[]],[],[],[]] => 1 [[[[]]],[],[],[]] => 2 [[[],[]],[],[[]]] => 2 [[[[]]],[],[[]]] => 3 [[[],[]],[[]],[]] => 2 [[[[]]],[[]],[]] => 3 [[[],[]],[[],[]]] => 2 [[[],[]],[[[]]]] => 3 [[[[]]],[[],[]]] => 3 [[[[]]],[[[]]]] => 4 [[[],[],[]],[],[]] => 1 [[[],[[]]],[],[]] => 2 [[[[]],[]],[],[]] => 2 [[[[],[]]],[],[]] => 2 [[[[[]]]],[],[]] => 3 [[[],[],[]],[[]]] => 2 [[[],[[]]],[[]]] => 3 [[[[]],[]],[[]]] => 3 [[[[],[]]],[[]]] => 3 [[[[[]]]],[[]]] => 4 [[[],[],[],[]],[]] => 1 [[[],[],[[]]],[]] => 2 [[[],[[]],[]],[]] => 2 [[[],[[],[]]],[]] => 2 [[[],[[[]]]],[]] => 3 [[[[]],[],[]],[]] => 2 [[[[]],[[]]],[]] => 3 [[[[],[]],[]],[]] => 2 [[[[[]]],[]],[]] => 3 [[[[],[],[]]],[]] => 2 [[[[],[[]]]],[]] => 3 [[[[[]],[]]],[]] => 3 [[[[[],[]]]],[]] => 3 [[[[[[]]]]],[]] => 4 [[[],[],[],[],[]]] => 1 [[[],[],[],[[]]]] => 2 [[[],[],[[]],[]]] => 2 [[[],[],[[],[]]]] => 2 [[[],[],[[[]]]]] => 3 [[[],[[]],[],[]]] => 2 [[[],[[]],[[]]]] => 3 [[[],[[],[]],[]]] => 2 [[[],[[[]]],[]]] => 3 [[[],[[],[],[]]]] => 2 [[[],[[],[[]]]]] => 3 [[[],[[[]],[]]]] => 3 [[[],[[[],[]]]]] => 3 [[[],[[[[]]]]]] => 4 [[[[]],[],[],[]]] => 2 [[[[]],[],[[]]]] => 3 [[[[]],[[]],[]]] => 3 [[[[]],[[],[]]]] => 3 [[[[]],[[[]]]]] => 4 [[[[],[]],[],[]]] => 2 [[[[[]]],[],[]]] => 3 [[[[],[]],[[]]]] => 3 [[[[[]]],[[]]]] => 4 [[[[],[],[]],[]]] => 2 [[[[],[[]]],[]]] => 3 [[[[[]],[]],[]]] => 3 [[[[[],[]]],[]]] => 3 [[[[[[]]]],[]]] => 4 [[[[],[],[],[]]]] => 2 [[[[],[],[[]]]]] => 3 [[[[],[[]],[]]]] => 3 [[[[],[[],[]]]]] => 3 [[[[],[[[]]]]]] => 4 [[[[[]],[],[]]]] => 3 [[[[[]],[[]]]]] => 4 [[[[[],[]],[]]]] => 3 [[[[[[]]],[]]]] => 4 [[[[[],[],[]]]]] => 3 [[[[[],[[]]]]]] => 4 [[[[[[]],[]]]]] => 4 [[[[[[],[]]]]]] => 4 [[[[[[[]]]]]]] => 5 ----------------------------------------------------------------------------- Created: Nov 09, 2013 at 01:04 by Viviane Pons ----------------------------------------------------------------------------- Last Updated: Apr 01, 2015 at 21:27 by Martin Rubey