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
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
KEYWORD
nonn
AUTHOR
Florian Deloup (deloup(AT)math.ups-tlse.fr), Sep 20 2006
STATUS
approved