Partitions into chains of a class of partially ordered sets

Metropolis, N.; Rota, Gian-Carlo; Strehl, Volker; White, Neil

doi:10.1090/S0002-9939-1978-0551483-6

Partitions into chains of a class of partially ordered sets
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by N. Metropolis, Gian-Carlo Rota, Volker Strehl and Neil White

Proc. Amer. Math. Soc. 71 (1978), 193-196

DOI: https://doi.org/10.1090/S0002-9939-1978-0551483-6

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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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