***************************************************************************** * 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: St000409 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The number of pitchforks in a binary tree. A pitchfork is a subtree of a complete binary tree with exactly three leaves, see Section 3.2 of [1]. ----------------------------------------------------------------------------- References: [1] Disanto, F., Wiehe, T. Exact enumeration of cherries and pitchforks in ranked trees under the coalescent model [[MathSciNet:3068684]] ----------------------------------------------------------------------------- Code: def statistic(B): if B == BinaryTree() or B == BinaryTree([]): return 0 if B == BinaryTree([[],None]) or B == BinaryTree([None, []]): return 1 return sum(statistic(S) for S in B) ----------------------------------------------------------------------------- Statistic values: [.,.] => 0 [.,[.,.]] => 1 [[.,.],.] => 1 [.,[.,[.,.]]] => 1 [.,[[.,.],.]] => 1 [[.,.],[.,.]] => 0 [[.,[.,.]],.] => 1 [[[.,.],.],.] => 1 [.,[.,[.,[.,.]]]] => 1 [.,[.,[[.,.],.]]] => 1 [.,[[.,.],[.,.]]] => 0 [.,[[.,[.,.]],.]] => 1 [.,[[[.,.],.],.]] => 1 [[.,.],[.,[.,.]]] => 1 [[.,.],[[.,.],.]] => 1 [[.,[.,.]],[.,.]] => 1 [[[.,.],.],[.,.]] => 1 [[.,[.,[.,.]]],.] => 1 [[.,[[.,.],.]],.] => 1 [[[.,.],[.,.]],.] => 0 [[[.,[.,.]],.],.] => 1 [[[[.,.],.],.],.] => 1 [.,[.,[.,[.,[.,.]]]]] => 1 [.,[.,[.,[[.,.],.]]]] => 1 [.,[.,[[.,.],[.,.]]]] => 0 [.,[.,[[.,[.,.]],.]]] => 1 [.,[.,[[[.,.],.],.]]] => 1 [.,[[.,.],[.,[.,.]]]] => 1 [.,[[.,.],[[.,.],.]]] => 1 [.,[[.,[.,.]],[.,.]]] => 1 [.,[[[.,.],.],[.,.]]] => 1 [.,[[.,[.,[.,.]]],.]] => 1 [.,[[.,[[.,.],.]],.]] => 1 [.,[[[.,.],[.,.]],.]] => 0 [.,[[[.,[.,.]],.],.]] => 1 [.,[[[[.,.],.],.],.]] => 1 [[.,.],[.,[.,[.,.]]]] => 1 [[.,.],[.,[[.,.],.]]] => 1 [[.,.],[[.,.],[.,.]]] => 0 [[.,.],[[.,[.,.]],.]] => 1 [[.,.],[[[.,.],.],.]] => 1 [[.,[.,.]],[.,[.,.]]] => 2 [[.,[.,.]],[[.,.],.]] => 2 [[[.,.],.],[.,[.,.]]] => 2 [[[.,.],.],[[.,.],.]] => 2 [[.,[.,[.,.]]],[.,.]] => 1 [[.,[[.,.],.]],[.,.]] => 1 [[[.,.],[.,.]],[.,.]] => 0 [[[.,[.,.]],.],[.,.]] => 1 [[[[.,.],.],.],[.,.]] => 1 [[.,[.,[.,[.,.]]]],.] => 1 [[.,[.,[[.,.],.]]],.] => 1 [[.,[[.,.],[.,.]]],.] => 0 [[.,[[.,[.,.]],.]],.] => 1 [[.,[[[.,.],.],.]],.] => 1 [[[.,.],[.,[.,.]]],.] => 1 [[[.,.],[[.,.],.]],.] => 1 [[[.,[.,.]],[.,.]],.] => 1 [[[[.,.],.],[.,.]],.] => 1 [[[.,[.,[.,.]]],.],.] => 1 [[[.,[[.,.],.]],.],.] => 1 [[[[.,.],[.,.]],.],.] => 0 [[[[.,[.,.]],.],.],.] => 1 [[[[[.,.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,.]]]]]] => 1 [.,[.,[.,[.,[[.,.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,.]]]]] => 0 [.,[.,[.,[[.,[.,.]],.]]]] => 1 [.,[.,[.,[[[.,.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,.]]]]] => 1 [.,[.,[[.,.],[[.,.],.]]]] => 1 [.,[.,[[.,[.,.]],[.,.]]]] => 1 [.,[.,[[[.,.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,.]]],.]]] => 1 [.,[.,[[.,[[.,.],.]],.]]] => 1 [.,[.,[[[.,.],[.,.]],.]]] => 0 [.,[.,[[[.,[.,.]],.],.]]] => 1 [.,[.,[[[[.,.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,.]]]]] => 1 [.,[[.,.],[.,[[.,.],.]]]] => 1 [.,[[.,.],[[.,.],[.,.]]]] => 0 [.,[[.,.],[[.,[.,.]],.]]] => 1 [.,[[.,.],[[[.,.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,.]]]] => 2 [.,[[.,[.,.]],[[.,.],.]]] => 2 [.,[[[.,.],.],[.,[.,.]]]] => 2 [.,[[[.,.],.],[[.,.],.]]] => 2 [.,[[.,[.,[.,.]]],[.,.]]] => 1 [.,[[.,[[.,.],.]],[.,.]]] => 1 [.,[[[.,.],[.,.]],[.,.]]] => 0 [.,[[[.,[.,.]],.],[.,.]]] => 1 [.,[[[[.,.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,.]]]],.]] => 1 [.,[[.,[.,[[.,.],.]]],.]] => 1 [.,[[.,[[.,.],[.,.]]],.]] => 0 [.,[[.,[[.,[.,.]],.]],.]] => 1 [.,[[.,[[[.,.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,.]]],.]] => 1 [.,[[[.,.],[[.,.],.]],.]] => 1 [.,[[[.,[.,.]],[.,.]],.]] => 1 [.,[[[[.,.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,.]]],.],.]] => 1 [.,[[[.,[[.,.],.]],.],.]] => 1 [.,[[[[.,.],[.,.]],.],.]] => 0 [.,[[[[.,[.,.]],.],.],.]] => 1 [.,[[[[[.,.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,.]]]]] => 1 [[.,.],[.,[.,[[.,.],.]]]] => 1 [[.,.],[.,[[.,.],[.,.]]]] => 0 [[.,.],[.,[[.,[.,.]],.]]] => 1 [[.,.],[.,[[[.,.],.],.]]] => 1 [[.,.],[[.,.],[.,[.,.]]]] => 1 [[.,.],[[.,.],[[.,.],.]]] => 1 [[.,.],[[.,[.,.]],[.,.]]] => 1 [[.,.],[[[.,.],.],[.,.]]] => 1 [[.,.],[[.,[.,[.,.]]],.]] => 1 [[.,.],[[.,[[.,.],.]],.]] => 1 [[.,.],[[[.,.],[.,.]],.]] => 0 [[.,.],[[[.,[.,.]],.],.]] => 1 [[.,.],[[[[.,.],.],.],.]] => 1 [[.,[.,.]],[.,[.,[.,.]]]] => 2 [[.,[.,.]],[.,[[.,.],.]]] => 2 [[.,[.,.]],[[.,.],[.,.]]] => 1 [[.,[.,.]],[[.,[.,.]],.]] => 2 [[.,[.,.]],[[[.,.],.],.]] => 2 [[[.,.],.],[.,[.,[.,.]]]] => 2 [[[.,.],.],[.,[[.,.],.]]] => 2 [[[.,.],.],[[.,.],[.,.]]] => 1 [[[.,.],.],[[.,[.,.]],.]] => 2 [[[.,.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,.]]],[.,[.,.]]] => 2 [[.,[.,[.,.]]],[[.,.],.]] => 2 [[.,[[.,.],.]],[.,[.,.]]] => 2 [[.,[[.,.],.]],[[.,.],.]] => 2 [[[.,.],[.,.]],[.,[.,.]]] => 1 [[[.,.],[.,.]],[[.,.],.]] => 1 [[[.,[.,.]],.],[.,[.,.]]] => 2 [[[.,[.,.]],.],[[.,.],.]] => 2 [[[[.,.],.],.],[.,[.,.]]] => 2 [[[[.,.],.],.],[[.,.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,.]] => 1 [[.,[.,[[.,.],.]]],[.,.]] => 1 [[.,[[.,.],[.,.]]],[.,.]] => 0 [[.,[[.,[.,.]],.]],[.,.]] => 1 [[.,[[[.,.],.],.]],[.,.]] => 1 [[[.,.],[.,[.,.]]],[.,.]] => 1 [[[.,.],[[.,.],.]],[.,.]] => 1 [[[.,[.,.]],[.,.]],[.,.]] => 1 [[[[.,.],.],[.,.]],[.,.]] => 1 [[[.,[.,[.,.]]],.],[.,.]] => 1 [[[.,[[.,.],.]],.],[.,.]] => 1 [[[[.,.],[.,.]],.],[.,.]] => 0 [[[[.,[.,.]],.],.],[.,.]] => 1 [[[[[.,.],.],.],.],[.,.]] => 1 [[.,[.,[.,[.,[.,.]]]]],.] => 1 [[.,[.,[.,[[.,.],.]]]],.] => 1 [[.,[.,[[.,.],[.,.]]]],.] => 0 [[.,[.,[[.,[.,.]],.]]],.] => 1 [[.,[.,[[[.,.],.],.]]],.] => 1 [[.,[[.,.],[.,[.,.]]]],.] => 1 [[.,[[.,.],[[.,.],.]]],.] => 1 [[.,[[.,[.,.]],[.,.]]],.] => 1 [[.,[[[.,.],.],[.,.]]],.] => 1 [[.,[[.,[.,[.,.]]],.]],.] => 1 [[.,[[.,[[.,.],.]],.]],.] => 1 [[.,[[[.,.],[.,.]],.]],.] => 0 [[.,[[[.,[.,.]],.],.]],.] => 1 [[.,[[[[.,.],.],.],.]],.] => 1 [[[.,.],[.,[.,[.,.]]]],.] => 1 [[[.,.],[.,[[.,.],.]]],.] => 1 [[[.,.],[[.,.],[.,.]]],.] => 0 [[[.,.],[[.,[.,.]],.]],.] => 1 [[[.,.],[[[.,.],.],.]],.] => 1 [[[.,[.,.]],[.,[.,.]]],.] => 2 [[[.,[.,.]],[[.,.],.]],.] => 2 [[[[.,.],.],[.,[.,.]]],.] => 2 [[[[.,.],.],[[.,.],.]],.] => 2 [[[.,[.,[.,.]]],[.,.]],.] => 1 [[[.,[[.,.],.]],[.,.]],.] => 1 [[[[.,.],[.,.]],[.,.]],.] => 0 [[[[.,[.,.]],.],[.,.]],.] => 1 [[[[[.,.],.],.],[.,.]],.] => 1 [[[.,[.,[.,[.,.]]]],.],.] => 1 [[[.,[.,[[.,.],.]]],.],.] => 1 [[[.,[[.,.],[.,.]]],.],.] => 0 [[[.,[[.,[.,.]],.]],.],.] => 1 [[[.,[[[.,.],.],.]],.],.] => 1 [[[[.,.],[.,[.,.]]],.],.] => 1 [[[[.,.],[[.,.],.]],.],.] => 1 [[[[.,[.,.]],[.,.]],.],.] => 1 [[[[[.,.],.],[.,.]],.],.] => 1 [[[[.,[.,[.,.]]],.],.],.] => 1 [[[[.,[[.,.],.]],.],.],.] => 1 [[[[[.,.],[.,.]],.],.],.] => 0 [[[[[.,[.,.]],.],.],.],.] => 1 [[[[[[.,.],.],.],.],.],.] => 1 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 0 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 1 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 1 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 1 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 0 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1 [.,[.,[.,[[[[.,.],.],.],.]]]] => 1 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 1 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 1 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 0 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 1 [.,[.,[[.,.],[[[.,.],.],.]]]] => 1 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2 [.,[.,[[[.,.],.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 1 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 1 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 0 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 1 [.,[.,[[[[.,.],.],.],[.,.]]]] => 1 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 0 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1 [.,[.,[[.,[[[.,.],.],.]],.]]] => 1 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 1 [.,[.,[[[.,.],[[.,.],.]],.]]] => 1 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 1 [.,[.,[[[[.,.],.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1 [.,[.,[[[.,[[.,.],.]],.],.]]] => 1 [.,[.,[[[[.,.],[.,.]],.],.]]] => 0 [.,[.,[[[[.,[.,.]],.],.],.]]] => 1 [.,[.,[[[[[.,.],.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 1 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 1 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 0 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 1 [.,[[.,.],[.,[[[.,.],.],.]]]] => 1 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 1 [.,[[.,.],[[.,.],[[.,.],.]]]] => 1 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 1 [.,[[.,.],[[[.,.],.],[.,.]]]] => 1 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 1 [.,[[.,.],[[.,[[.,.],.]],.]]] => 1 [.,[[.,.],[[[.,.],[.,.]],.]]] => 0 [.,[[.,.],[[[.,[.,.]],.],.]]] => 1 [.,[[.,.],[[[[.,.],.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 1 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2 [.,[[.,[.,.]],[[[.,.],.],.]]] => 2 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2 [.,[[[.,.],.],[.,[[.,.],.]]]] => 2 [.,[[[.,.],.],[[.,.],[.,.]]]] => 1 [.,[[[.,.],.],[[.,[.,.]],.]]] => 2 [.,[[[.,.],.],[[[.,.],.],.]]] => 2 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2 [.,[[.,[[.,.],.]],[[.,.],.]]] => 2 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 1 [.,[[[.,.],[.,.]],[[.,.],.]]] => 1 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 2 [.,[[[.,[.,.]],.],[[.,.],.]]] => 2 [.,[[[[.,.],.],.],[.,[.,.]]]] => 2 [.,[[[[.,.],.],.],[[.,.],.]]] => 2 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 1 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 1 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 0 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 1 [.,[[.,[[[.,.],.],.]],[.,.]]] => 1 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 1 [.,[[[.,.],[[.,.],.]],[.,.]]] => 1 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 1 [.,[[[[.,.],.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 1 [.,[[[.,[[.,.],.]],.],[.,.]]] => 1 [.,[[[[.,.],[.,.]],.],[.,.]]] => 0 [.,[[[[.,[.,.]],.],.],[.,.]]] => 1 [.,[[[[[.,.],.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 0 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1 [.,[[.,[.,[[[.,.],.],.]]],.]] => 1 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 1 [.,[[.,[[.,.],[[.,.],.]]],.]] => 1 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 1 [.,[[.,[[[.,.],.],[.,.]]],.]] => 1 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1 [.,[[.,[[.,[[.,.],.]],.]],.]] => 1 [.,[[.,[[[.,.],[.,.]],.]],.]] => 0 [.,[[.,[[[.,[.,.]],.],.]],.]] => 1 [.,[[.,[[[[.,.],.],.],.]],.]] => 1 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 1 [.,[[[.,.],[.,[[.,.],.]]],.]] => 1 [.,[[[.,.],[[.,.],[.,.]]],.]] => 0 [.,[[[.,.],[[.,[.,.]],.]],.]] => 1 [.,[[[.,.],[[[.,.],.],.]],.]] => 1 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 2 [.,[[[.,[.,.]],[[.,.],.]],.]] => 2 [.,[[[[.,.],.],[.,[.,.]]],.]] => 2 [.,[[[[.,.],.],[[.,.],.]],.]] => 2 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 1 [.,[[[.,[[.,.],.]],[.,.]],.]] => 1 [.,[[[[.,.],[.,.]],[.,.]],.]] => 0 [.,[[[[.,[.,.]],.],[.,.]],.]] => 1 [.,[[[[[.,.],.],.],[.,.]],.]] => 1 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1 [.,[[[.,[.,[[.,.],.]]],.],.]] => 1 [.,[[[.,[[.,.],[.,.]]],.],.]] => 0 [.,[[[.,[[.,[.,.]],.]],.],.]] => 1 [.,[[[.,[[[.,.],.],.]],.],.]] => 1 [.,[[[[.,.],[.,[.,.]]],.],.]] => 1 [.,[[[[.,.],[[.,.],.]],.],.]] => 1 [.,[[[[.,[.,.]],[.,.]],.],.]] => 1 [.,[[[[[.,.],.],[.,.]],.],.]] => 1 [.,[[[[.,[.,[.,.]]],.],.],.]] => 1 [.,[[[[.,[[.,.],.]],.],.],.]] => 1 [.,[[[[[.,.],[.,.]],.],.],.]] => 0 [.,[[[[[.,[.,.]],.],.],.],.]] => 1 [.,[[[[[[.,.],.],.],.],.],.]] => 1 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 0 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 1 [[.,.],[.,[.,[[[.,.],.],.]]]] => 1 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 1 [[.,.],[.,[[.,.],[[.,.],.]]]] => 1 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 1 [[.,.],[.,[[[.,.],.],[.,.]]]] => 1 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 1 [[.,.],[.,[[.,[[.,.],.]],.]]] => 1 [[.,.],[.,[[[.,.],[.,.]],.]]] => 0 [[.,.],[.,[[[.,[.,.]],.],.]]] => 1 [[.,.],[.,[[[[.,.],.],.],.]]] => 1 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 1 [[.,.],[[.,.],[.,[[.,.],.]]]] => 1 [[.,.],[[.,.],[[.,.],[.,.]]]] => 0 [[.,.],[[.,.],[[.,[.,.]],.]]] => 1 [[.,.],[[.,.],[[[.,.],.],.]]] => 1 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,.]],[[.,.],.]]] => 2 [[.,.],[[[.,.],.],[.,[.,.]]]] => 2 [[.,.],[[[.,.],.],[[.,.],.]]] => 2 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 1 [[.,.],[[.,[[.,.],.]],[.,.]]] => 1 [[.,.],[[[.,.],[.,.]],[.,.]]] => 0 [[.,.],[[[.,[.,.]],.],[.,.]]] => 1 [[.,.],[[[[.,.],.],.],[.,.]]] => 1 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 1 [[.,.],[[.,[.,[[.,.],.]]],.]] => 1 [[.,.],[[.,[[.,.],[.,.]]],.]] => 0 [[.,.],[[.,[[.,[.,.]],.]],.]] => 1 [[.,.],[[.,[[[.,.],.],.]],.]] => 1 [[.,.],[[[.,.],[.,[.,.]]],.]] => 1 [[.,.],[[[.,.],[[.,.],.]],.]] => 1 [[.,.],[[[.,[.,.]],[.,.]],.]] => 1 [[.,.],[[[[.,.],.],[.,.]],.]] => 1 [[.,.],[[[.,[.,[.,.]]],.],.]] => 1 [[.,.],[[[.,[[.,.],.]],.],.]] => 1 [[.,.],[[[[.,.],[.,.]],.],.]] => 0 [[.,.],[[[[.,[.,.]],.],.],.]] => 1 [[.,.],[[[[[.,.],.],.],.],.]] => 1 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 1 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2 [[.,[.,.]],[.,[[[.,.],.],.]]] => 2 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2 [[.,[.,.]],[[.,.],[[.,.],.]]] => 2 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2 [[.,[.,.]],[[[.,.],.],[.,.]]] => 2 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2 [[.,[.,.]],[[.,[[.,.],.]],.]] => 2 [[.,[.,.]],[[[.,.],[.,.]],.]] => 1 [[.,[.,.]],[[[.,[.,.]],.],.]] => 2 [[.,[.,.]],[[[[.,.],.],.],.]] => 2 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2 [[[.,.],.],[.,[.,[[.,.],.]]]] => 2 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[[[.,[.,.]],.],[.,[[.,.],.]]] => 2 [[[.,[.,.]],.],[[.,.],[.,.]]] => 1 [[[.,[.,.]],.],[[.,[.,.]],.]] => 2 [[[.,[.,.]],.],[[[.,.],.],.]] => 2 [[[[.,.],.],.],[.,[.,[.,.]]]] => 2 [[[[.,.],.],.],[.,[[.,.],.]]] => 2 [[[[.,.],.],.],[[.,.],[.,.]]] => 1 [[[[.,.],.],.],[[.,[.,.]],.]] => 2 [[[[.,.],.],.],[[[.,.],.],.]] => 2 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2 [[.,[.,[[.,.],.]]],[[.,.],.]] => 2 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 1 [[.,[[.,.],[.,.]]],[[.,.],.]] => 1 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2 [[.,[[.,[.,.]],.]],[[.,.],.]] => 2 [[.,[[[.,.],.],.]],[.,[.,.]]] => 2 [[.,[[[.,.],.],.]],[[.,.],.]] => 2 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2 [[[.,.],[.,[.,.]]],[[.,.],.]] => 2 [[[.,.],[[.,.],.]],[.,[.,.]]] => 2 [[[.,.],[[.,.],.]],[[.,.],.]] => 2 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2 [[[.,[.,.]],[.,.]],[[.,.],.]] => 2 [[[[.,.],.],[.,.]],[.,[.,.]]] => 2 [[[[.,.],.],[.,.]],[[.,.],.]] => 2 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2 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[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => 1 [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => 1 [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => 2 [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => 1 ----------------------------------------------------------------------------- Created: Feb 25, 2016 at 09:05 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 12, 2018 at 23:47 by Martin Rubey