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A122555 Number of isomorphism classes of linking pairings on finite Abelian 2-groups of fixed order 2^n. 1

%I

%S 1,4,6,14,20,43,59,108,158,265,373,600,838,1301,1797,2693,3695,5379,

%T 7291,10407,14023,19651,26227,36166,47888,65193,85731,115308,150598,

%U 200420

%N Number of isomorphism classes of linking pairings on finite Abelian 2-groups of fixed order 2^n.

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

%C 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.

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

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

%H F. Deloup, <a href="http://www.msp.warwick.ac.uk/agt/2005/05/p019.xhtml">Monoide des enlacements et facteurs orthogonaux</a>.

%H F. Deloup, <a href="/A122555/a122555.txt">Maple program</a>

%e 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.

%K nonn

%O 1,2

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

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