***************************************************************************** * 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: St001563 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The value of the power-sum symmetric function evaluated at 1. The statistic is $p_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=x_2=\dotsb=x_k$, where $\lambda$ has $k$ parts. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 4 [3] => 1 [2,1] => 4 [1,1,1] => 27 [4] => 1 [3,1] => 4 [2,2] => 4 [2,1,1] => 27 [1,1,1,1] => 256 [5] => 1 [4,1] => 4 [3,2] => 4 [3,1,1] => 27 [2,2,1] => 27 [2,1,1,1] => 256 [1,1,1,1,1] => 3125 [6] => 1 [5,1] => 4 [4,2] => 4 [4,1,1] => 27 [3,3] => 4 [3,2,1] => 27 [3,1,1,1] => 256 [2,2,2] => 27 [2,2,1,1] => 256 [2,1,1,1,1] => 3125 [1,1,1,1,1,1] => 46656 [7] => 1 [6,1] => 4 [5,2] => 4 [5,1,1] => 27 [4,3] => 4 [4,2,1] => 27 [4,1,1,1] => 256 [3,3,1] => 27 [3,2,2] => 27 [3,2,1,1] => 256 [3,1,1,1,1] => 3125 [2,2,2,1] => 256 [2,2,1,1,1] => 3125 [2,1,1,1,1,1] => 46656 [1,1,1,1,1,1,1] => 823543 ----------------------------------------------------------------------------- Created: Jul 11, 2020 at 10:03 by Per Alexandersson ----------------------------------------------------------------------------- Last Updated: Jul 11, 2020 at 10:03 by Per Alexandersson