***************************************************************************** * 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: St001564 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The value of the forgotten symmetric functions when all variables set to 1. Let $f_\lambda(x)$ denote the forgotten symmetric functions. Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts, is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 3 [3] => 1 [2,1] => 6 [1,1,1] => 10 [4] => 1 [3,1] => 6 [2,2] => 3 [2,1,1] => 30 [1,1,1,1] => 35 [5] => 1 [4,1] => 6 [3,2] => 6 [3,1,1] => 30 [2,2,1] => 30 [2,1,1,1] => 140 [1,1,1,1,1] => 126 [6] => 1 [5,1] => 6 [4,2] => 6 [4,1,1] => 30 [3,3] => 3 [3,2,1] => 60 [3,1,1,1] => 140 [2,2,2] => 10 [2,2,1,1] => 210 [2,1,1,1,1] => 630 [1,1,1,1,1,1] => 462 [7] => 1 [6,1] => 6 [5,2] => 6 [5,1,1] => 30 [4,3] => 6 [4,2,1] => 60 [4,1,1,1] => 140 [3,3,1] => 30 [3,2,2] => 30 [3,2,1,1] => 420 [3,1,1,1,1] => 630 [2,2,2,1] => 140 [2,2,1,1,1] => 1260 [2,1,1,1,1,1] => 2772 [1,1,1,1,1,1,1] => 1716 ----------------------------------------------------------------------------- Created: Jul 11, 2020 at 09:56 by Per Alexandersson ----------------------------------------------------------------------------- Last Updated: Jul 11, 2020 at 09:56 by Per Alexandersson