# formatting symmetries of solid partitions for EIS

wouter meeussen wouter.meeussen at pandora.be
Thu Jun 24 23:49:12 CEST 2004

```dear seqs,

I get three symmetry operations for solid partitions,
flip (mirror), rotate and the funny 'time-lapse'.

How to incorporate'm into EIS so that future lookers can find them?

Cycle lengths seem relevant (Cauchy-frobenius...), but I'm out of depth and could be shadow-boxing
here. Anyone got access to the existing stuff, and suggest how to turn this into 'retreavable' seqs?

Flip:
tot {count, cycles} ..
1 {1, 1}  {0, 2}
4 {2, 1}  {1, 2}
10 {4, 1}  {3, 2}
26 {8, 1}  {9, 2}
59 {13, 1}  {23, 2}
140 {24, 1}  {58, 2}
307 {39, 1}  {134, 2}
684 {68, 1}  {308, 2}
1464 {110, 1} {677, 2}
3122 {182, 1} {1470, 2}
6500 {288, 1} {3106, 2}
13426 {468, 1} {6479, 2}

Rotate:
1 {1, 1} {0, 3}
4 {1, 1} {1, 3}
10 {1, 1} {3, 3}
26 {2, 1} {8, 3}
59 {2, 1} {19, 3}
140 {2, 1} {46, 3}
307 {4, 1} {101, 3}
684 {6, 1} {226, 3}
1464 {6, 1} {486, 3}
3122 {8, 1} {1038, 3}
6500 {11, 1} {2163, 3}
13426 {13, 1} {4471, 3}

'time Lapse'
1 {1, 1} {0, 2} {0, 4}
4 {1, 4} {0, 2} {0, 4}
10 {1, 2} {0, 2} {2, 4}
26 {1, 2} {0, 2} {6, 4}
59 {1, 1} {1, 2} {14, 4}
140 {2, 2} {0, 2} {34, 4}
307 {1, 1} {3, 2} {75, 4}
684 {6, 2} {0, 2} {168, 4}
1464 {2, 1} {7, 2} {362, 4}
3122 {11, 2} {0, 2} {775, 4}
6500 {2, 1} {15, 2} {1617, 4}
13426 {25, 2} {0, 2} {3344, 4}

partitions are nice, aren't they?
W.

```