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Journal of the London Mathematical Society 1997 55(3):417-426; doi:10.1112/S0024610797004821
© 1997 by London Mathematical Society
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© The London Mathematical Society

Ordering Integer Vectors for Coordinate Deletions

Tran-Ngoc Danh and David E. Daykin

Department of Mathematics, University of Ho Chi Min City Ho Chi Min City, Vietnam
Department of Mathematics, University of Reading

Received 15 February 1994.

Given a family of sets/vectors of the same cardinality/dimension you get the shadow by deleting one element/coordinate from a set/vector in all possible ways. You find the family with the smallest shadow by ordering all sets/vectors. The set case was solved by Kruskal (1963), and Katona (1966), and has many applications. We study two orderings which solve the 0, 1 vector case, and give the shadow size.

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