***************************************************************************** * 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: St001203 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: In the list $L$ delete the first entry $c_0$ and substract from all other entries $n-1$ and then append the last element 1 (this was suggested by Christian Stump). The result is a Kupisch series of an LNakayama algebra. Example: [5,6,6,6,6] goes into [2,2,2,2,1]. Now associate to the CNakayama algebra with the above properties the Dyck path corresponding to the Kupisch series of the LNakayama algebra. The statistic return the global dimension of the CNakayama algebra divided by 2. ----------------------------------------------------------------------------- References: [1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 2 [1,1,0,0] => 1 [1,0,1,0,1,0] => 3 [1,0,1,1,0,0] => 2 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,0] => 4 [1,0,1,0,1,1,0,0,1,0] => 4 [1,0,1,0,1,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0] => 4 [1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,1,1,0,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,0] => 3 [1,0,1,1,0,1,1,0,0,0,1,0] => 4 [1,0,1,1,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,0] => 3 [1,0,1,1,1,0,0,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0,1,0] => 3 [1,0,1,1,1,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,0,1,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,0,1,0] => 4 [1,1,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0] => 3 [1,1,0,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,1,1,0,0,0,1,1,0,0] => 3 [1,1,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,0] => 3 [1,1,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,0] => 2 [1,1,0,1,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0,1,0] => 4 [1,1,1,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,0,1,1,0,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4 [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4 [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4 [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4 [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4 [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4 [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4 [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4 [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 4 [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3 [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4 [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3 [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4 [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 4 [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4 [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3 [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4 [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4 [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4 [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3 [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5 [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3 [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3 [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4 [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4 [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4 [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3 [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4 [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3 [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4 [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3 [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3 [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3 [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3 [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3 [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5 [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4 [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3 [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3 [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3 [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3 [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5 [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4 [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3 [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4 [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3 [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4 [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3 [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4 [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4 [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3 [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3 [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3 [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3 [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3 [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4 [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3 [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4 [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2 [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3 [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3 [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 3 [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3 [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2 [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: May 15, 2018 at 11:02 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 16, 2018 at 10:29 by Rene Marczinzik