Each irreducible representation [λ] of the symmetric group Sn may be identified by a partition [λ] of n into non-negative integral parts λ1 ≥ λ2 ≥ … λn ≥ 0, of which the first λ'j parts are ≥j, or by a right (Young) diagram also called [λ], that contains λi nodes in its ith row and λ'j nodes in its jth column.

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In 1984, the Texas Legislature funded a four-university, interdisciplinary effort to identify feasible sites for location of a very high-energy physics lab in Texas and to evaluate the comparative advantages of one site versus another. Six feasible sites were identified and a comparative site analysis was made by applying Data Envelopment Analysis (DEA), incorporating project cost, user time delay, and environmental impact data. In addition, for the efficient sites, the price weights for user time delay and environmental impact, given normalization on project cost, were analyzed and arguments were developed to bracket these pairs of price weights into an “assurance region” for the preferred site(s). The South Dallas site was found to be preferred for a wide range of conditions, while the North Houston site was sensitive to the method of indexing the impact of the environment. The method appears to be applicable to a wide range of siting problems faced by not only government, but also industry.

This paper gives a formulation of a theory of n‐person cooperative games with side payments in terms of a partition function which is defined on the set of all partitions of the set of players. The results for all games with n ≤ 3 are presented. This development generalizes the von Neumann‐Morgenstern theory of games in characteristic function form.

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