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A198210
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Frequency of different patterns of permutation's cycles in transitive group PZL(2,16) of order 8160.
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0
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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
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OFFSET
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1,7
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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}
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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