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Identifier
Values
=>
Cc0002;cc-rep
[2]=>1 [1,1]=>1 [3]=>1 [2,1]=>4 [1,1,1]=>1 [4]=>1 [3,1]=>9 [2,2]=>4 [2,1,1]=>9 [1,1,1,1]=>1 [5]=>1 [4,1]=>16 [3,2]=>25 [3,1,1]=>36 [2,2,1]=>25 [2,1,1,1]=>16 [1,1,1,1,1]=>1 [6]=>1 [5,1]=>25 [4,2]=>81 [4,1,1]=>100 [3,3]=>25 [3,2,1]=>256 [3,1,1,1]=>100 [2,2,2]=>25 [2,2,1,1]=>81 [2,1,1,1,1]=>25 [1,1,1,1,1,1]=>1 [7]=>1 [6,1]=>36 [5,2]=>196 [5,1,1]=>225 [4,3]=>196 [4,2,1]=>1225 [4,1,1,1]=>400 [3,3,1]=>441 [3,2,2]=>441 [3,2,1,1]=>1225 [3,1,1,1,1]=>225 [2,2,2,1]=>196 [2,2,1,1,1]=>196 [2,1,1,1,1,1]=>36 [1,1,1,1,1,1,1]=>1 [8]=>1 [7,1]=>49 [6,2]=>400 [6,1,1]=>441 [5,3]=>784 [5,2,1]=>4096 [5,1,1,1]=>1225 [4,4]=>196 [4,3,1]=>4900 [4,2,2]=>3136 [4,2,1,1]=>8100 [4,1,1,1,1]=>1225 [3,3,2]=>1764 [3,3,1,1]=>3136 [3,2,2,1]=>4900 [3,2,1,1,1]=>4096 [3,1,1,1,1,1]=>441 [2,2,2,2]=>196 [2,2,2,1,1]=>784 [2,2,1,1,1,1]=>400 [2,1,1,1,1,1,1]=>49 [1,1,1,1,1,1,1,1]=>1 [9]=>1 [8,1]=>64 [7,2]=>729 [7,1,1]=>784 [6,3]=>2304 [6,2,1]=>11025 [6,1,1,1]=>3136 [5,4]=>1764 [5,3,1]=>26244 [5,2,2]=>14400 [5,2,1,1]=>35721 [5,1,1,1,1]=>4900 [4,4,1]=>7056 [4,3,2]=>28224 [4,3,1,1]=>46656 [4,2,2,1]=>46656 [4,2,1,1,1]=>35721 [4,1,1,1,1,1]=>3136 [3,3,3]=>1764 [3,3,2,1]=>28224 [3,3,1,1,1]=>14400 [3,2,2,2]=>7056 [3,2,2,1,1]=>26244 [3,2,1,1,1,1]=>11025 [3,1,1,1,1,1,1]=>784 [2,2,2,2,1]=>1764 [2,2,2,1,1,1]=>2304 [2,2,1,1,1,1,1]=>729 [2,1,1,1,1,1,1,1]=>64 [1,1,1,1,1,1,1,1,1]=>1 [10]=>1 [9,1]=>81 [8,2]=>1225 [8,1,1]=>1296 [7,3]=>5625 [7,2,1]=>25600 [7,1,1,1]=>7056 [6,4]=>8100 [6,3,1]=>99225 [6,2,2]=>50625 [6,2,1,1]=>122500 [6,1,1,1,1]=>15876 [5,5]=>1764 [5,4,1]=>82944 [5,3,2]=>202500 [5,3,1,1]=>321489 [5,2,2,1]=>275625 [5,2,1,1,1]=>200704 [5,1,1,1,1,1]=>15876 [4,4,2]=>63504 [4,4,1,1]=>90000 [4,3,3]=>44100 [4,3,2,1]=>589824 [4,3,1,1,1]=>275625 [4,2,2,2]=>90000 [4,2,2,1,1]=>321489 [4,2,1,1,1,1]=>122500 [4,1,1,1,1,1,1]=>7056 [3,3,3,1]=>44100 [3,3,2,2]=>63504 [3,3,2,1,1]=>202500 [3,3,1,1,1,1]=>50625 [3,2,2,2,1]=>82944 [3,2,2,1,1,1]=>99225 [3,2,1,1,1,1,1]=>25600 [3,1,1,1,1,1,1,1]=>1296 [2,2,2,2,2]=>1764 [2,2,2,2,1,1]=>8100 [2,2,2,1,1,1,1]=>5625 [2,2,1,1,1,1,1,1]=>1225 [2,1,1,1,1,1,1,1,1]=>81 [1,1,1,1,1,1,1,1,1,1]=>1 [11]=>1 [10,1]=>100 [9,2]=>1936 [9,1,1]=>2025 [8,3]=>12100 [8,2,1]=>53361 [8,1,1,1]=>14400 [7,4]=>27225 [7,3,1]=>302500 [7,2,2]=>148225 [7,2,1,1]=>352836 [7,1,1,1,1]=>44100 [6,5]=>17424 [6,4,1]=>480249 [6,3,2]=>980100 [6,3,1,1]=>1517824 [6,2,2,1]=>1210000 [6,2,1,1,1]=>853776 [6,1,1,1,1,1]=>63504 [5,5,1]=>108900 [5,4,2]=>980100 [5,4,1,1]=>1334025 [5,3,3]=>435600 [5,3,2,1]=>5336100 [5,3,1,1,1]=>2371600 [5,2,2,2]=>680625 [5,2,2,1,1]=>2371600 [5,2,1,1,1,1]=>853776 [5,1,1,1,1,1,1]=>44100 [4,4,3]=>213444 [4,4,2,1]=>1742400 [4,4,1,1,1]=>680625 [4,3,3,1]=>1411344 [4,3,2,2]=>1742400 [4,3,2,1,1]=>5336100 [4,3,1,1,1,1]=>1210000 [4,2,2,2,1]=>1334025 [4,2,2,1,1,1]=>1517824 [4,2,1,1,1,1,1]=>352836 [4,1,1,1,1,1,1,1]=>14400 [3,3,3,2]=>213444 [3,3,3,1,1]=>435600 [3,3,2,2,1]=>980100 [3,3,2,1,1,1]=>980100 [3,3,1,1,1,1,1]=>148225 [3,2,2,2,2]=>108900 [3,2,2,2,1,1]=>480249 [3,2,2,1,1,1,1]=>302500 [3,2,1,1,1,1,1,1]=>53361 [3,1,1,1,1,1,1,1,1]=>2025 [2,2,2,2,2,1]=>17424 [2,2,2,2,1,1,1]=>27225 [2,2,2,1,1,1,1,1]=>12100 [2,2,1,1,1,1,1,1,1]=>1936 [2,1,1,1,1,1,1,1,1,1]=>100 [1,1,1,1,1,1,1,1,1,1,1]=>1 [12]=>1 [11,1]=>121 [10,2]=>2916 [10,1,1]=>3025 [9,3]=>23716 [9,2,1]=>102400 [9,1,1,1]=>27225 [8,4]=>75625 [8,3,1]=>793881 [8,2,2]=>379456 [8,2,1,1]=>893025 [8,1,1,1,1]=>108900 [7,5]=>88209 [7,4,1]=>1982464 [7,3,2]=>3705625 [7,3,1,1]=>5645376 [7,2,2,1]=>4322241 [7,2,1,1,1]=>2985984 [7,1,1,1,1,1]=>213444 [6,6]=>17424 [6,5,1]=>1334025 [6,4,2]=>7144929 [6,4,1,1]=>9486400 [6,3,3]=>2722500 [6,3,2,1]=>31719424 [6,3,1,1,1]=>13660416 [6,2,2,2]=>3705625 [6,2,2,1,1]=>12702096 [6,2,1,1,1,1]=>4410000 [6,1,1,1,1,1,1]=>213444 [5,5,2]=>1742400 [5,5,1,1]=>2205225 [5,4,3]=>4460544 [5,4,2,1]=>33350625 [5,4,1,1,1]=>12390400 [5,3,3,1]=>17288964 [5,3,2,2]=>19847025 [5,3,2,1,1]=>59290000 [5,3,1,1,1,1]=>12702096 [5,2,2,2,1]=>12390400 [5,2,2,1,1,1]=>13660416 [5,2,1,1,1,1,1]=>2985984 [5,1,1,1,1,1,1,1]=>108900 [4,4,4]=>213444 [4,4,3,1]=>8820900 [4,4,2,2]=>6969600 [4,4,2,1,1]=>19847025 [4,4,1,1,1,1]=>3705625 [4,3,3,2]=>8820900 [4,3,3,1,1]=>17288964 [4,3,2,2,1]=>33350625 [4,3,2,1,1,1]=>31719424 [4,3,1,1,1,1,1]=>4322241 [4,2,2,2,2]=>2205225 [4,2,2,2,1,1]=>9486400 [4,2,2,1,1,1,1]=>5645376 [4,2,1,1,1,1,1,1]=>893025 [4,1,1,1,1,1,1,1,1]=>27225 [3,3,3,3]=>213444 [3,3,3,2,1]=>4460544 [3,3,3,1,1,1]=>2722500 [3,3,2,2,2]=>1742400 [3,3,2,2,1,1]=>7144929 [3,3,2,1,1,1,1]=>3705625 [3,3,1,1,1,1,1,1]=>379456 [3,2,2,2,2,1]=>1334025 [3,2,2,2,1,1,1]=>1982464 [3,2,2,1,1,1,1,1]=>793881 [3,2,1,1,1,1,1,1,1]=>102400 [3,1,1,1,1,1,1,1,1,1]=>3025 [2,2,2,2,2,2]=>17424 [2,2,2,2,2,1,1]=>88209 [2,2,2,2,1,1,1,1]=>75625 [2,2,2,1,1,1,1,1,1]=>23716 [2,2,1,1,1,1,1,1,1,1]=>2916 [2,1,1,1,1,1,1,1,1,1,1]=>121 [1,1,1,1,1,1,1,1,1,1,1,1]=>1
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Description
The Plancherel distribution on integer partitions.
This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions.
Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.
Code
def statistic(L):
    return L.standard_tableaux().cardinality()^2
Created
Sep 15, 2015 at 08:40 by Martin Rubey
Updated
Jul 12, 2017 at 10:03 by Christian Stump