Gómez Soto, José Manuel; Leaños, Jesús; Ríos Castro, Luis Manuel; Rivera Martínez, Luis Manuel
Resumen:
Neil Sloane showed that the problem of determining the maximum size of a binary code of
constant weight 2 that can correct a single adjacent transposition is equivalent to finding
the packing number of a certain graph. In this paper we solve this open problem by finding
the packing number of the double vertex graph of the path graph. This double vertex graph
is isomorphic to Sloane’s graph. Our solution implies a conjecture of Rob Pratt about the
ordinary generating function of sequence A085680.