184,621 research outputs found
Conformal Designs based on Vertex Operator Algebras
We introduce the notion of a conformal design based on a vertex operator
algebra. This notation is a natural analog of the notion of block designs or
spherical designs when the elements of the design are based on self-orthogonal
binary codes or integral lattices, respectively. It is shown that the subspaces
of fixed degree of an extremal self-dual vertex operator algebra form conformal
11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and
Venkov for extremal doubly-even codes and extremal even lattices. Other
examples are coming from group actions on vertex operator algebras, the case
studied first by Matsuo. The classification of conformal 6- and 8-designs is
investigated. Again, our results are analogous to similar results for codes and
lattices.Comment: 35 pages with 1 table, LaTe
The Intersection problem for 2-(v; 5; 1) directed block designs
The intersection problem for a pair of 2-(v, 3, 1) directed designs and 2-(v,
4, 1) directed designs is solved by Fu in 1983 and by Mahmoodian and Soltankhah
in 1996, respectively. In this paper we determine the intersection problem for
2-(v, 5, 1) directed designs.Comment: 17 pages. To appear in Discrete Mat
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