Memoir on the theory of the partitions of numbers.—part IV. On the probability that the successful candidate at an election by ballot may never at any time have fewer votes than the one who is unsuccessful; on a generalization of this question: and on its connexion with other question of partition, permutation, and combination

Abstract

1. Consider a lattice in two dimensions, taking, for instance,one in which AB, BC are 7 and 5 segments in length respectively. It may be utilised for the study of permutations, combinations, and partitions in various ways, also for the study of certain questions in the theory of probabilities. 2. A "line of route" through the latttice from A to C may be traced by moving over horizontal segments ( α segments) in the direction AB, and over vertical segments ( β segments) in the direction BC in any order. Thus one line of route is ADEFGHIC.