***************************************************************************** * 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: St000041 ----------------------------------------------------------------------------- Collection: Perfect matchings ----------------------------------------------------------------------------- Description: The number of nestings of a perfect matching. This is the number of pairs of edges \$((a,b), (c,d))\$ such that \$a\le c\le d\le b\$. i.e., the edge \$(c,d)\$ is nested inside \$(a,b)\$. ----------------------------------------------------------------------------- References: [1] de Médicis, A., Viennot, X. G. Moments des \$q\$-polynômes de Laguerre et la bijection de Foata-Zeilberger [[MathSciNet:1288802]] [2] Simion, R., Stanton, D. Octabasic Laguerre polynomials and permutation statistics [[MathSciNet:1418763]] ----------------------------------------------------------------------------- Code: def statistic(x): return len(x.nestings()) ----------------------------------------------------------------------------- Statistic values: [(1,2)] => 0 [(1,2),(3,4)] => 0 [(1,3),(2,4)] => 0 [(1,4),(2,3)] => 1 [(1,2),(3,4),(5,6)] => 0 [(1,2),(3,5),(4,6)] => 0 [(1,2),(3,6),(4,5)] => 1 [(1,3),(2,4),(5,6)] => 0 [(1,3),(2,5),(4,6)] => 0 [(1,3),(2,6),(4,5)] => 1 [(1,4),(2,3),(5,6)] => 1 [(1,4),(2,5),(3,6)] => 0 [(1,4),(2,6),(3,5)] => 1 [(1,5),(2,3),(4,6)] => 1 [(1,5),(2,4),(3,6)] => 1 [(1,5),(2,6),(3,4)] => 2 [(1,6),(2,3),(4,5)] => 2 [(1,6),(2,4),(3,5)] => 2 [(1,6),(2,5),(3,4)] => 3 [(1,2),(3,4),(5,8),(6,7)] => 1 [(1,2),(3,4),(5,7),(6,8)] => 0 [(1,2),(3,4),(5,6),(7,8)] => 0 [(1,2),(3,5),(4,8),(6,7)] => 1 [(1,2),(3,5),(4,7),(6,8)] => 0 [(1,2),(3,5),(4,6),(7,8)] => 0 [(1,2),(3,6),(4,8),(5,7)] => 1 [(1,2),(3,6),(4,7),(5,8)] => 0 [(1,2),(3,6),(4,5),(7,8)] => 1 [(1,2),(3,7),(4,8),(5,6)] => 2 [(1,2),(3,7),(4,6),(5,8)] => 1 [(1,2),(3,7),(4,5),(6,8)] => 1 [(1,2),(3,8),(4,5),(6,7)] => 2 [(1,2),(3,8),(4,6),(5,7)] => 2 [(1,2),(3,8),(4,7),(5,6)] => 3 [(1,3),(2,4),(5,8),(6,7)] => 1 [(1,3),(2,4),(5,7),(6,8)] => 0 [(1,3),(2,4),(5,6),(7,8)] => 0 [(1,3),(2,5),(4,8),(6,7)] => 1 [(1,3),(2,5),(4,7),(6,8)] => 0 [(1,3),(2,5),(4,6),(7,8)] => 0 [(1,3),(2,6),(4,8),(5,7)] => 1 [(1,3),(2,6),(4,7),(5,8)] => 0 [(1,3),(2,6),(4,5),(7,8)] => 1 [(1,3),(2,7),(4,8),(5,6)] => 2 [(1,3),(2,7),(4,6),(5,8)] => 1 [(1,3),(2,7),(4,5),(6,8)] => 1 [(1,3),(2,8),(4,5),(6,7)] => 2 [(1,3),(2,8),(4,6),(5,7)] => 2 [(1,3),(2,8),(4,7),(5,6)] => 3 [(1,4),(2,3),(5,8),(6,7)] => 2 [(1,4),(2,3),(5,7),(6,8)] => 1 [(1,4),(2,3),(5,6),(7,8)] => 1 [(1,4),(2,5),(3,8),(6,7)] => 1 [(1,4),(2,5),(3,7),(6,8)] => 0 [(1,4),(2,5),(3,6),(7,8)] => 0 [(1,4),(2,6),(3,8),(5,7)] => 1 [(1,4),(2,6),(3,7),(5,8)] => 0 [(1,4),(2,6),(3,5),(7,8)] => 1 [(1,4),(2,7),(3,8),(5,6)] => 2 [(1,4),(2,7),(3,6),(5,8)] => 1 [(1,4),(2,7),(3,5),(6,8)] => 1 [(1,4),(2,8),(3,5),(6,7)] => 2 [(1,4),(2,8),(3,6),(5,7)] => 2 [(1,4),(2,8),(3,7),(5,6)] => 3 [(1,5),(2,3),(4,8),(6,7)] => 2 [(1,5),(2,3),(4,7),(6,8)] => 1 [(1,5),(2,3),(4,6),(7,8)] => 1 [(1,5),(2,4),(3,8),(6,7)] => 2 [(1,5),(2,4),(3,7),(6,8)] => 1 [(1,5),(2,4),(3,6),(7,8)] => 1 [(1,5),(2,6),(3,8),(4,7)] => 1 [(1,5),(2,6),(3,7),(4,8)] => 0 [(1,5),(2,6),(3,4),(7,8)] => 2 [(1,5),(2,7),(3,8),(4,6)] => 2 [(1,5),(2,7),(3,6),(4,8)] => 1 [(1,5),(2,7),(3,4),(6,8)] => 2 [(1,5),(2,8),(3,4),(6,7)] => 3 [(1,5),(2,8),(3,6),(4,7)] => 2 [(1,5),(2,8),(3,7),(4,6)] => 3 [(1,6),(2,3),(4,8),(5,7)] => 2 [(1,6),(2,3),(4,7),(5,8)] => 1 [(1,6),(2,3),(4,5),(7,8)] => 2 [(1,6),(2,4),(3,8),(5,7)] => 2 [(1,6),(2,4),(3,7),(5,8)] => 1 [(1,6),(2,4),(3,5),(7,8)] => 2 [(1,6),(2,5),(3,8),(4,7)] => 2 [(1,6),(2,5),(3,7),(4,8)] => 1 [(1,6),(2,5),(3,4),(7,8)] => 3 [(1,6),(2,7),(3,8),(4,5)] => 3 [(1,6),(2,7),(3,5),(4,8)] => 2 [(1,6),(2,7),(3,4),(5,8)] => 2 [(1,6),(2,8),(3,4),(5,7)] => 3 [(1,6),(2,8),(3,5),(4,7)] => 3 [(1,6),(2,8),(3,7),(4,5)] => 4 [(1,7),(2,3),(4,8),(5,6)] => 3 [(1,7),(2,3),(4,6),(5,8)] => 2 [(1,7),(2,3),(4,5),(6,8)] => 2 [(1,7),(2,4),(3,8),(5,6)] => 3 [(1,7),(2,4),(3,6),(5,8)] => 2 [(1,7),(2,4),(3,5),(6,8)] => 2 [(1,7),(2,5),(3,8),(4,6)] => 3 [(1,7),(2,5),(3,6),(4,8)] => 2 [(1,7),(2,5),(3,4),(6,8)] => 3 [(1,7),(2,6),(3,8),(4,5)] => 4 [(1,7),(2,6),(3,5),(4,8)] => 3 [(1,7),(2,6),(3,4),(5,8)] => 3 [(1,7),(2,8),(3,4),(5,6)] => 4 [(1,7),(2,8),(3,5),(4,6)] => 4 [(1,7),(2,8),(3,6),(4,5)] => 5 [(1,8),(2,3),(4,5),(6,7)] => 3 [(1,8),(2,3),(4,6),(5,7)] => 3 [(1,8),(2,3),(4,7),(5,6)] => 4 [(1,8),(2,4),(3,5),(6,7)] => 3 [(1,8),(2,4),(3,6),(5,7)] => 3 [(1,8),(2,4),(3,7),(5,6)] => 4 [(1,8),(2,5),(3,4),(6,7)] => 4 [(1,8),(2,5),(3,6),(4,7)] => 3 [(1,8),(2,5),(3,7),(4,6)] => 4 [(1,8),(2,6),(3,4),(5,7)] => 4 [(1,8),(2,6),(3,5),(4,7)] => 4 [(1,8),(2,6),(3,7),(4,5)] => 5 [(1,8),(2,7),(3,4),(5,6)] => 5 [(1,8),(2,7),(3,5),(4,6)] => 5 [(1,8),(2,7),(3,6),(4,5)] => 6 [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1 [(1,2),(3,4),(5,6),(7,9),(8,10)] => 0 [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0 [(1,2),(3,4),(5,7),(6,9),(8,10)] => 0 [(1,2),(3,4),(5,7),(6,8),(9,10)] => 0 [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1 [(1,2),(3,4),(5,8),(6,9),(7,10)] => 0 [(1,2),(3,4),(5,10),(6,7),(8,9)] => 2 [(1,2),(3,4),(5,10),(6,9),(7,8)] => 3 [(1,2),(3,5),(4,6),(7,9),(8,10)] => 0 [(1,2),(3,5),(4,6),(7,8),(9,10)] => 0 [(1,2),(3,5),(4,7),(6,9),(8,10)] => 0 [(1,2),(3,5),(4,7),(6,8),(9,10)] => 0 [(1,2),(3,5),(4,8),(6,9),(7,10)] => 0 [(1,2),(3,6),(4,5),(7,10),(8,9)] => 2 [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1 [(1,2),(3,6),(4,7),(5,9),(8,10)] => 0 [(1,2),(3,6),(4,7),(5,8),(9,10)] => 0 [(1,2),(3,6),(4,8),(5,9),(7,10)] => 0 [(1,2),(3,7),(4,8),(5,9),(6,10)] => 0 [(1,2),(3,8),(4,5),(6,7),(9,10)] => 2 [(1,2),(3,8),(4,7),(5,6),(9,10)] => 3 [(1,2),(3,10),(4,5),(6,7),(8,9)] => 3 [(1,2),(3,10),(4,5),(6,9),(7,8)] => 4 [(1,2),(3,10),(4,7),(5,6),(8,9)] => 4 [(1,2),(3,10),(4,9),(5,8),(6,7)] => 6 [(1,2),(3,10),(4,9),(5,6),(7,8)] => 5 [(1,3),(2,4),(5,6),(7,9),(8,10)] => 0 [(1,3),(2,4),(5,6),(7,8),(9,10)] => 0 [(1,3),(2,4),(5,7),(6,9),(8,10)] => 0 [(1,3),(2,4),(5,7),(6,8),(9,10)] => 0 [(1,3),(2,4),(5,8),(6,9),(7,10)] => 0 [(1,3),(2,5),(4,6),(7,9),(8,10)] => 0 [(1,3),(2,5),(4,6),(7,8),(9,10)] => 0 [(1,3),(2,5),(4,7),(6,9),(8,10)] => 0 [(1,3),(2,5),(4,7),(6,8),(9,10)] => 0 [(1,3),(2,5),(4,8),(6,9),(7,10)] => 0 [(1,3),(2,6),(4,7),(5,9),(8,10)] => 0 [(1,3),(2,6),(4,7),(5,8),(9,10)] => 0 [(1,3),(2,6),(4,8),(5,9),(7,10)] => 0 [(1,3),(2,7),(4,8),(5,9),(6,10)] => 0 [(1,4),(2,3),(5,6),(7,10),(8,9)] => 2 [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1 [(1,4),(2,3),(5,8),(6,7),(9,10)] => 2 [(1,4),(2,3),(5,10),(6,7),(8,9)] => 3 [(1,4),(2,3),(5,10),(6,9),(7,8)] => 4 [(1,4),(2,5),(3,6),(7,9),(8,10)] => 0 [(1,4),(2,5),(3,6),(7,8),(9,10)] => 0 [(1,4),(2,5),(3,7),(6,9),(8,10)] => 0 [(1,4),(2,5),(3,7),(6,8),(9,10)] => 0 [(1,4),(2,5),(3,8),(6,9),(7,10)] => 0 [(1,4),(2,6),(3,7),(5,9),(8,10)] => 0 [(1,4),(2,6),(3,7),(5,8),(9,10)] => 0 [(1,4),(2,6),(3,8),(5,9),(7,10)] => 0 [(1,4),(2,7),(3,8),(5,9),(6,10)] => 0 [(1,5),(2,6),(3,7),(4,9),(8,10)] => 0 [(1,5),(2,6),(3,7),(4,8),(9,10)] => 0 [(1,5),(2,6),(3,8),(4,9),(7,10)] => 0 [(1,5),(2,7),(3,8),(4,9),(6,10)] => 0 [(1,6),(2,3),(4,5),(7,10),(8,9)] => 3 [(1,6),(2,3),(4,5),(7,8),(9,10)] => 2 [(1,6),(2,5),(3,4),(7,10),(8,9)] => 4 [(1,6),(2,5),(3,4),(7,8),(9,10)] => 3 [(1,6),(2,7),(3,8),(4,9),(5,10)] => 0 [(1,8),(2,3),(4,5),(6,7),(9,10)] => 3 [(1,8),(2,3),(4,7),(5,6),(9,10)] => 4 [(1,8),(2,5),(3,4),(6,7),(9,10)] => 4 [(1,8),(2,7),(3,4),(5,6),(9,10)] => 5 [(1,8),(2,7),(3,6),(4,5),(9,10)] => 6 [(1,10),(2,3),(4,5),(6,7),(8,9)] => 4 [(1,10),(2,3),(4,5),(6,9),(7,8)] => 5 [(1,10),(2,3),(4,7),(5,6),(8,9)] => 5 [(1,10),(2,3),(4,9),(5,8),(6,7)] => 7 [(1,10),(2,3),(4,9),(5,6),(7,8)] => 6 [(1,10),(2,5),(3,4),(6,7),(8,9)] => 5 [(1,10),(2,5),(3,4),(6,9),(7,8)] => 6 [(1,10),(2,7),(3,4),(5,6),(8,9)] => 6 [(1,10),(2,7),(3,6),(4,5),(8,9)] => 7 [(1,10),(2,9),(3,4),(5,8),(6,7)] => 8 [(1,10),(2,9),(3,4),(5,6),(7,8)] => 7 [(1,10),(2,9),(3,6),(4,5),(7,8)] => 8 [(1,10),(2,9),(3,8),(4,5),(6,7)] => 9 [(1,10),(2,9),(3,8),(4,7),(5,6)] => 10 [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 15 [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 6 [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => 8 [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 7 [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 7 [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => 10 [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 1 [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => 9 [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 8 [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 2 [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => 9 [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 2 [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 8 [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 3 [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => 12 [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 3 [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => 5 [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 4 [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 4 [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => 11 [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 2 [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => 10 [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 9 [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 3 [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => 6 [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 3 [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 5 [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 4 [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => 11 [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 2 [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => 6 [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 5 [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 3 [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => 10 [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 3 [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 9 [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 4 [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => 7 [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 4 [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 4 [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 5 [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 5 [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => 14 [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 5 [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => 7 [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 6 [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 6 [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => 9 [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0 [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => 8 [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 7 [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 1 [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => 8 [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 1 [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 7 [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 2 [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => 13 [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 4 [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => 6 [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 5 [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 5 [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => 12 [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 3 [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => 11 [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 10 [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 4 [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => 7 [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 4 [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 6 [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 5 [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => 10 [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 1 [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => 7 [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 6 [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 2 [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => 9 [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 2 [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 8 [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 3 [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => 8 [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 5 [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 3 [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 6 [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 4 [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => 13 [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 4 [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => 6 [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 5 [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 5 [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => 10 [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 1 [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => 9 [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 8 [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 2 [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => 7 [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 2 [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 6 [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 3 [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => 12 [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 3 [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => 7 [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 6 [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 4 [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => 11 [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 4 [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 10 [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 5 [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => 8 [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 3 [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 5 [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 4 [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 6 [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => 11 [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 2 [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => 8 [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 7 [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 3 [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => 8 [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 3 [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 7 [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 4 [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => 9 [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 6 [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 4 [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 7 [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 5 [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => 9 [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 4 [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 6 [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 5 [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 7 [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 6 [(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => 0 [(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => 0 [(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => 0 [(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => 0 [(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => 0 [(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => 0 [(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => 0 [(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => 0 [(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => 0 [(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => 0 [(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => 0 [(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => 0 [(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => 0 [(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => 0 [(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => 0 [(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => 0 [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => 0 [(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => 0 [(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => 0 [(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => 0 [(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => 0 [(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => 0 [(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => 0 [(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => 0 [(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => 0 [(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => 0 [(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => 0 [(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => 0 [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => 0 [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => 0 [(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => 0 [(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => 0 [(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => 0 [(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => 0 [(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => 0 [(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => 0 [(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => 0 [(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => 0 [(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => 0 [(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => 0 [(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => 0 [(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => 0 [(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => 0 [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => 0 [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => 0 [(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => 0 [(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => 0 [(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => 0 [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => 0 [(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => 0 [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => 0 [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => 0 [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => 0 [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => 0 [(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => 0 [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => 0 [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => 0 [(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => 0 [(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => 0 [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => 0 [(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => 0 [(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => 0 [(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => 0 [(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => 0 [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => 0 [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => 0 [(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => 0 [(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => 0 [(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => 0 [(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => 0 [(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => 0 [(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => 0 [(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => 0 [(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => 0 [(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => 0 [(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => 0 [(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => 0 [(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => 0 [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => 0 [(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => 0 [(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => 0 [(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => 0 [(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => 0 [(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => 0 [(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => 0 [(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => 0 [(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => 0 [(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => 0 [(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => 0 [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => 0 [(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => 0 [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => 0 [(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => 0 [(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => 0 [(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => 0 [(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => 0 [(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => 0 [(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => 0 [(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => 0 [(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => 0 [(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => 0 [(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => 0 [(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => 0 [(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => 0 [(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => 0 [(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => 0 [(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => 0 [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => 0 [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => 0 [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => 0 [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => 0 [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => 0 [(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => 0 [(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => 0 [(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => 0 [(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => 0 [(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => 0 [(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => 0 [(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => 0 [(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => 0 [(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => 0 [(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => 0 [(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => 0 [(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => 0 [(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => 0 [(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => 0 [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => 0 [(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => 0 [(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => 0 [(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => 0 [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => 0 [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 11 [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 11 [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 12 [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 11 [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 11 [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 12 [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 13 [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 11 [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 12 [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 13 [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 14 [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 15 [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 11 [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => 11 [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => 11 [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 12 [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => 11 [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => 11 [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 12 [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 13 [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 11 [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 11 [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 12 [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 13 [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 14 [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 15 [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 18 [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 18 [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 19 [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 18 [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 19 [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 20 [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 21 [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => 18 [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => 18 [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => 19 [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 18 [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => 19 [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 20 [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 21 [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => 28 [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 28 [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)] => 27 [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 27 [(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)] => 26 [(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)] => 26 [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 26 [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 26 [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)] => 36 [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 36 [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)] => 35 [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 35 [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)] => 45 [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 45 ----------------------------------------------------------------------------- Created: Mar 01, 2013 at 02:34 by Alejandro Morales ----------------------------------------------------------------------------- Last Updated: Dec 25, 2017 at 17:15 by Martin Rubey