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A122555 Number of isomorphism classes of linking pairings on finite Abelian 2-groups of fixed order 2^n. 1
1, 4, 6, 14, 20, 43, 59, 108, 158, 265, 373, 600, 838, 1301, 1797, 2693, 3695, 5379, 7291, 10407, 14023, 19651, 26227, 36166, 47888, 65193, 85731, 115308, 150598, 200420 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A linking pairing on a finite Abelian group G is a nonsingular symmetric bilinear form G x G --> Q/Z.

The combinatorics of this sequence are surprisingly complicated. The corresponding case when p is odd is easier and is now understood. The sequence is a combinatorial refinement of partitions of integers.

REFERENCES

F. Deloup, Monoide des enlacements et facteurs orthogonaux, Algebraic and Geometric Topology, 5 (2005) 419-442.

A. Kawauchi and S. Kojima, Algebraic classification of linking pairings on 3-manifolds, Math. Ann. 253 (1980), 29-42.

LINKS

Table of n, a(n) for n=1..30.

F. Deloup, Monoide des enlacements et facteurs orthogonaux.

F. Deloup, Maple program

EXAMPLE

a(2) = 4 because there are 4 nonequivalent linking pairings on finite Abelian groups of order 2^2 = 4: there are two nonequivalent cyclic pairings on Z/4, one direct product of two cyclic pairings on Z/2 and one noncyclic pairing on Z/2 x Z/2.

CROSSREFS

Sequence in context: A310649 A310650 A310651 * A210632 A097271 A126867

Adjacent sequences:  A122552 A122553 A122554 * A122556 A122557 A122558

KEYWORD

nonn

AUTHOR

Florian Deloup (deloup(AT)math.ups-tlse.fr), Sep 20 2006

STATUS

approved

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)