21,111 research outputs found
Series expansions without diagrams
We discuss the use of recursive enumeration schemes to obtain low and high
temperature series expansions for discrete statistical systems. Using linear
combinations of generalized helical lattices, the method is competitive with
diagramatic approaches and is easily generalizable. We illustrate the approach
using the Ising model and generate low temperature series in up to five
dimensions and high temperature series in three dimensions. The method is
general and can be applied to any discrete model. We describe how it would work
for Potts models.Comment: 24 pages, IASSNS-HEP-93/1
Perfect single error-correcting codes in the Johnson Scheme
Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the
Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be
k-regular for large k, and used this to show that there are no perfect codes
correcting single errors in J(n,w) for n <= 50000. In this paper we show that
there are no perfect single error-correcting codes for n <= 2^250.Comment: 4 pages, revised, accepted for publication in IEEE Transactions on
Information Theor
- …