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Partitions into chains of a class of partially ordered sets

Authors: N. Metropolis, Gian-Carlo Rota, Volker Strehl and Neil White
Journal: Proc. Amer. Math. Soc. 71 (1978), 193-196
MSC: Primary 06A10; Secondary 05B99
MathSciNet review: 0551483
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Abstract: Let a cube of side k in $ {{\mathbf{R}}^n}$ be dissected into $ {k^n}$ unit cubes. The collection of all affine subspaces of $ {{\mathbf{R}}^n}$ determined by the faces of the unit cubes forms a lattice $ L(n,k)$ when ordered by inclusion. We explicitly construct a Dilworth partition into chains of $ L(n,k)$.

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Article copyright: © Copyright 1978 American Mathematical Society

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