The Collected Mathematical Papers of James Joseph Sylvester, F.R.S.

Abstract

THE longest items in this final volume are the “constructive theory of partitions,” published in The American Journal, and the lectures on reciprocants. The first of these is more consecutive than the notes on Sylvester's King's College course printed in a previous volume; perhaps, for this very reason, it is not quite so interesting. But his use of graphs is most ingenious, and the occurrence of Farey series in this connection may be specially noted. It is a rather curious fact that at the end of Art. 17 (pp. 15-16), Sylvester says that he has not proved a theorem there stated about resolving N into sets of sequences. The theorem actually follows from the most elementary considerations; the only reason that can be suggested for Sylvester miss-ing the proof is that he failed to note a one-one correspondence between two arithmetical expres-sions for sets of numbers.

The Collected Mathematical Papers of James Joseph Sylvester, F.R.S.

Vol. iv. (1882”97). Pp. xxxviii + 756. (Cambridge University Press, 1912.); 18s. net.