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The enumeration of all possible cases is thus reduced to a simple question in combinatorial analysis, and the actual study of any particular case is much facilitated by a useful rule of Klein’s for writing down in a simple form two quadratics belonging to a given class—one of which, of course, represents the equation connecting line coordinates, and the other the equation of the complex.

For more advanced treatment of linear indeterminate equations see Combinatorial Analysis.

Professor James Waddell Alexander will lecture on combinatorial analysis situs, hold seminars on the applications of algebra and group theory to topology.

The Combinatorial Analysis, as it was understood up to the end of the 18th century, was of limited scope and restricted application.

Interest in England was aroused, in the first instance, by Augustus De Morgan in 1846, who, in a letter to Henry Warburton, suggested that combinatorial analysis stood in great need of development, and alluded to the theory of partitions.