A198210 Frequency of different patterns of permutation's cycles in transitive group PZL(2,16) of order 8160.

1, 0, 0, 0, 0, 0, 68, 0, 255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,7

Comments

These patterns p_n are successive ordered integer partitions of number 17 on sum of integers.

p_1= {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},

p_2= {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2},

p_297={17}

Group PZL(2,16) is Galois group over rationals for some polynomials of 17 degree. Anyone sample isn't know up to now (these is smallest order group with unknown example).

Links

Table of n, a(n) for n=1..84.

Example

a(1)=1 because group contained only one permutation with pattern a_1={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}.
a(7)=68 because in group are 68 different permutations of 17 elements with pattern p_7={1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2}

Crossrefs

Sequence in context: A087536 A281888 A282338 * A329061 A033388 A196109

Adjacent sequences: A198207 A198208 A198209 * A198211 A198212 A198213

Keyword

uned,nonn,fini

Author

Artur Jasinski, Oct 22 2011

Status

approved