Frank Lübeck   

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Elementary Divisors for Partitions of n = 10

PartitionSpecht degreeelementary divisors
(23,14)75[25*32] [27*32]8 [27*32*7]18 [28*32*7]7 [28*33*7]41 
(24,12)90[25*32] [25*32*7]34 [25*32*5*7]13 [26*32*5*7]26 [27*32*5*7]16 
(25)42[25*32*5]8 [25*32*52]18 [26*32*52]15 [26*33*52
(3,2,15)160[23*3*5]34 [23*33*5]2 [23*33*5*7]40 [23*34*5*7]84 
(3,22,13)315[23*3]36 [23*32]12 [24*32]26 [26*32]17 [27*32]26 [28*32]43 [28*32*5]155 
(3,23,1)288[22*3]8 [22*3*5]63 [22*3*52]18 [22*3*52*7]71 [23*3*52*7]119 [23*32*52*7]9 
(32,14)225[24*3]26 [26*3] [27*3]72 [27*32]25 [27*32*7]101 
(32,2,12)450[24]66 [24*7]158 [25*7]16 [26*7]10 [27*7]29 [27*3*7]45 [27*32*7]126 
(32,22)252[23] [23*5]25 [24*5]26 [25*5]38 [25*3*5]126 [25*32*5]2 [25*32*52]34 
(33,1)210[23*3]8 [24*3]33 [24*32]85 [24*33]29 [24*33*5]55 
(4,2,14)350[23*3]26 [24*3]58 [24*32]42 [24*34]98 [25*34]58 [26*34]68 
(4,22,12)567[22]28 [22*5]170 [23*5]26 [24*5]17 [25*5]60 [25*52]8 [26*52]58 [27*52]200 
(4,23)300[22*3]26 [23*3]15 [23*32]59 [24*32]99 [24*32*7]67 [24*33*7]34 
(4,3,13)525[2*3]42 [2*32]156 [24*32] [25*32]102 [25*33]168 [26*33]56 
(4,3,2,1)768[1]41 [3]176 [3*5]167 [32*5*7]167 [32*52*7]176 [33*52*7]41 
(4,32)210[23]55 [23*5]29 [23*3*5]85 [23*32*5]33 [24*32*5]8 
(42,12)300[22]34 [22*3]67 [22*3*7]99 [23*3*7]59 [23*32*7]15 [24*32*7]26 
(42,2)252[2]34 [2*5]2 [2*3*5]126 [2*32*5]38 [22*32*5]26 [23*32*5]25 [23*32*52
(5,2,13)448[2*3]56 [2*3*5]168 [2*33*5]168 [2*33*52]56 
(5,22,1)525[22]56 [23]168 [23*3]102 [24*3] [27*3]156 [27*32]42 
(5,3,12)567[2]200 [22]58 [23]8 [23*5]60 [24*5]17 [25*5]26 [26*5]170 [26*52]28 
(5,3,2)450[1]126 [3]45 [32]29 [2*32]10 [22*32]16 [23*32]158 [23*32*7]66 
(5,4,1)288[1]9 [3]119 [2*3]71 [2*3*7]18 [2*3*5*7]63 [2*3*52*7]8 
(52)42[2] [2*3]15 [22*3]18 [22*3*5]8 
(6,2,12)350[2]68 [22]58 [23]98 [23*32]42 [23*33]58 [24*33]26 
(6,22)225[2]101 [2*7]25 [2*3*7]72 [22*3*7] [24*3*7]26 
(6,3,1)315[1]155 [5]43 [2*5]26 [22*5]17 [24*5]26 [25*5]12 [25*3*5]36 
(6,4)90[1]16 [2]26 [22]13 [22*5]34 [22*5*7] 
(7,2,1)160[1]84 [3]40 [3*7]2 [33*7]34 
(7,3)75[1]41 [3]7 [2*3]18 [2*3*7]8 [23*3*7] 

Known Jantzen Filtrations

PartitionPrime Jantzen Filtration
(110)2 [D(10)]8
(110)3 [D(52)]4
(110)5 [D(32,22)]2
(110)7 [D(24,12)]1
(2,18)2 [D(10)]7 +[D(9,1)]8
(2,18)3 [D(5,4,1)]2
(2,18)5 [D(32,22)]1 +[D(3,23,1)]2
(2,18)7 [D(23,14)]1
(22,16)2 [D(9,1)]5 +[D(10)]6 +[D(8,2)]8
(22,16)3 [D(52)]2 +[D(42,12)]4
(22,16)5 [D(24,12)]1
(23,14)2 [D(10)]5 +[D(8,2)]7 +[D(7,3)]8
(23,14)3 [D(42,12)]2 +[D(4,3,2,1)]3
(23,14)7 [D(23,14)]0 +[D(32,2,12)]1
(24,12)2 [D(7,3)]5 +[D(8,2)]6 +[D(6,4)]7
(24,12)3 [D(32,22)]2
(24,12)5 [D(24,12)]0 +[D(4,32)]1
(24,12)7 [D(24,12)]0 +[D(3,23,1)]1
(25)2 [D(8,2)]5 +[D(6,4)]6
(25)3 [D(4,3,2,1)]2 +[D(10)]3
(25)5 [D(3,23,1)]1 +[D(42,2)]2
(3,17)2 [D(9,1)]4 +[D(8,2)+2*D(10)]5
(3,17)3 [D(42,2)]2
(3,17)5 [D(3,23,1)]1 +[D(4,22,12)]2
(3,17)7 [D(3,2,15)]1
(3,2,15)2 [D(7,2,1)]3
(3,2,15)3 [D(42,12)]1 +[D(4,3,2,1)+D(52)]3 +[D(4,32)]4
(3,2,15)5 [D(3,22,13)]1
(3,2,15)7 [D(3,2,15)]0 +[D(32,14)]1
(3,22,13)2 [D(7,3)]3 +[D(8,2)]4 +[D(6,4)+D(10)]6 +[D(8,2)]7 +[D(6,3,1)]8
(3,22,13)3 [D(42,2)]1 +[D(32,2,12)]2
(3,22,13)5 [D(3,22,13)]0 +[D(33,1)]1
(3,23,1)2 [D(7,2,1)]2 +[D(5,4,1)]3
(3,23,1)3 [D(32,2,12)]1 +[D(9,1)]2
(3,23,1)5 [D(3,23,1)]0 +[D(32,22)+D(4,22,12)+D(42,2)]1 +[D(4,3,2,1)]2
(3,23,1)7 [D(3,23,1)]0 +[D(4,23)]1
(32,14)2 [D(8,2)]4 +[D(10)]6 +[D(6,3,1)]7
(32,14)3 [D(32,22)+D(5,4,1)]1 +[D(5,3,2)]2
(32,14)7 [D(32,14)]0 +[D(42,12)]1
(32,2,12)2 [D(6,3,1)+D(8,2)]4 +[D(6,4)]5 +[D(9,1)+2*D(10)]6 +[D(5,3,2)]7
(32,2,12)3 [D(32,2,12)]0 +[D(42,2)+D(9,1)]1 +[D(6,22)]2
(32,2,12)7 [D(32,2,12)]0 +[D(4,3,2,1)]1
(32,22)3 [D(32,22)]0 +[D(5,3,2)]1 +[D(8,12)]2
(32,22)5 [D(32,22)]0 +[D(4,3,2,1)]1 +[D(52)]2
(33,1)2 [D(9,1)]3 +[D(5,3,2)+2*D(10)]4
(33,1)5 [D(33,1)]0 +[D(6,4)]1
(4,16)2 [D(8,2)+2*D(10)]4 +[D(7,3)+D(9,1)]5
(4,16)3 [D(4,32)]2
(4,16)5 [D(4,22,12)]1 +[D(5,2,13)]2
(4,2,14)2 [D(8,2)]3 +[D(6,3,1)]4 +[D(7,3)+D(9,1)+2*D(10)]5 +[D(6,4)+2*D(8,2)]6
(4,2,14)3 [D(4,32)]1 +[D(4,3,2,1)+D(52)]2 +[D(5,22,1)]4
(4,22,12)2 [D(6,3,1)]2 +[D(8,2)]3 +[D(6,4)+D(10)]4 +[D(6,4)+2*D(8,2)]5 +[D(7,3)+D(9,1)+2*D(10)]6 +[D(5,3,2)]7
(4,22,12)5 [D(4,22,12)]0 +[D(4,3,2,1)+D(5,2,13)]1 +[D(5,3,12)]2
(4,23)3 [D(4,3,2,1)]1 +[D(5,22,1)+D(10)]2 +[D(8,2)]3
(4,23)7 [D(4,23)]0 +[D(6,22)]1
(4,3,13)2 [D(6,3,1)]1 +[D(10)]4 +[D(5,3,2)+D(6,4)+2*D(8,2)+2*D(10)]5 +[D(7,3)+D(9,1)]6
(4,3,2,1)5 [D(4,3,2,1)]0 +[D(42,2)+D(5,3,12)+D(52)]1 +[D(5,4,1)]2
(4,3,2,1)7 [D(4,3,2,1)]0 +[D(5,3,2)]1
(4,32)2 [D(5,3,2)+2*D(10)]3 +[D(9,1)]4
(4,32)3 [D(4,32)]0 +[D(52)+D(7,2,1)]1 +[D(7,3)]2
(4,32)5 [D(4,32)]0 +[D(6,3,1)]1
(42,12)3 [D(42,12)]0 +[D(52)+D(6,2,12)]1 +[D(7,3)]2
(42,12)7 [D(42,12)]0 +[D(5,4,1)]1
(42,2)3 [D(42,2)]0 +[D(6,22)]1 +[D(6,4)]2
(42,2)5 [D(42,2)]0 +[D(5,4,1)]1 +[D(10)]2
(5,15)2 [D(7,3)+D(9,1)]3 +[D(6,4)+2*D(8,2)+2*D(10)]4
(5,15)3 [D(5,3,2)]1
(5,15)5 [D(5,2,13)]1 +[D(6,14)]2
(5,2,13)2 [D(5,4,1)+2*D(7,2,1)]1
(5,2,13)5 [D(5,2,13)]0 +[D(5,3,12)+D(6,14)]1 +[D(7,13)]2
(5,22,1)2 [D(7,3)+D(9,1)]2 +[D(5,3,2)+D(6,4)+2*D(8,2)+2*D(10)]3 +[D(10)]4 +[D(6,3,1)]7
(5,3,12)2 [D(5,3,2)]1 +[D(7,3)+D(9,1)+2*D(10)]2 +[D(6,4)+2*D(8,2)]3 +[D(6,4)+D(10)]4 +[D(8,2)]5 +[D(6,3,1)]6
(5,3,12)5 [D(5,3,12)]0 +[D(5,4,1)+D(7,13)]1 +[D(8,12)]2
(5,3,2)2 [D(5,3,2)]0 +[D(9,1)+2*D(10)]1 +[D(6,4)]2 +[D(6,3,1)+D(8,2)]3
(5,3,2)3 [D(5,3,2)]0 +[D(5,4,1)+D(8,12)]1 +[D(6,3,1)]2
(5,3,2)7 [D(5,3,2)]0 +[D(7,3)]1
(5,4,1)2 [D(5,4,1)]0 +[D(7,2,1)]1
(5,4,1)3 [D(5,4,1)]0 +[D(6,3,1)]1
(5,4,1)5 [D(5,4,1)]0 +[D(52)+D(8,12)+D(10)]1 +[D(9,1)]2
(5,4,1)7 [D(5,4,1)]0 +[D(6,4)]1
(52)2 [D(6,4)]1 +[D(8,2)]2
(52)3 [D(52)]0 +[D(7,3)]1
(52)5 [D(52)]0 +[D(9,1)]1
(6,14)2 [D(6,4)+2*D(8,2)+2*D(10)]3 +[D(7,3)+D(9,1)]4
(6,14)3 [D(6,22)]1
(6,14)5 [D(6,14)]0 +[D(7,13)]1
(6,2,12)2 [D(6,4)+2*D(8,2)]1 +[D(7,3)+D(9,1)+2*D(10)]2 +[D(6,3,1)]3 +[D(8,2)]4
(6,2,12)3 [D(6,2,12)]0 +[D(7,3)+D(10)]2 +[D(7,2,1)]3
(6,22)2 [D(6,3,1)]1 +[D(10)]2 +[D(8,2)]4
(6,22)3 [D(6,22)]0 +[D(6,4)+D(9,1)]1
(6,22)7 [D(6,22)]0 +[D(7,2,1)]1
(6,3,1)2 [D(6,3,1)]0 +[D(8,2)]1 +[D(6,4)+D(10)]2 +[D(8,2)]4 +[D(7,3)]5
(6,3,1)3 [D(6,3,1)]0 +[D(8,12)]1
(6,3,1)5 [D(6,3,1)]0 +[D(7,2,1)]1
(6,4)2 [D(6,4)]0 +[D(8,2)]1 +[D(7,3)]2
(6,4)5 [D(6,4)]0 +[D(8,2)]1
(6,4)7 [D(6,4)]0 +[D(10)]1
(7,13)2 [D(7,3)+D(9,1)]1 +[D(8,2)+2*D(10)]2
(7,13)3 [D(7,2,1)]1
(7,13)5 [D(7,13)]0 +[D(8,12)]1
(7,2,1)3 [D(7,2,1)]0 +[D(7,3)+D(10)]1 +[D(8,2)]3
(7,2,1)7 [D(7,2,1)]0 +[D(8,12)]1
(7,3)2 [D(7,3)]0 +[D(8,2)]1 +[D(10)]3
(7,3)3 [D(7,3)]0 +[D(8,2)]1
(7,3)7 [D(7,3)]0 +[D(9,1)]1
(8,12)2 [D(8,2)+2*D(10)]1 +[D(9,1)]2
(8,12)5 [D(8,12)]0 +[D(9,1)]1
(8,2)2 [D(8,2)]0 +[D(10)]2 +[D(9,1)]3
(8,2)3 [D(8,2)]0 +[D(10)]2
(9,1)2 [D(9,1)]0 +[D(10)]1
(9,1)5 [D(9,1)]0 +[D(10)]1

Last updated: Mon Jul 12 23:23:19 2004 (CET)