Linear Rankings of Finite Dimensional PatternsStanford University, Stanford Electronics Laboratories, Systems Theory Laboratory, 1966 - Linear topological spaces - 23 pages The paper determines Q(n, d), the number of ways that n d-dimensional pattern vectors can be ordered by projection onto a freely-chosen weighting vector. This is equivalent to finding the number of ways of ranking n students on the basis of arbitrary linear combinations of their scores on d examinations. Q(n, d) is independent (subject to minor nonsingularity constraints) of the precise configuration of the pattern vectors, and is naturally expressible as a sum of stirling-like numbers. (Author). |
