## 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 PDF
- Proc. Amer. Math. Soc.
**71**(1978), 193-196 Request permission

## 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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## Additional Information

- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**71**(1978), 193-196 - MSC: Primary 06A10; Secondary 05B99
- DOI: https://doi.org/10.1090/S0002-9939-1978-0551483-6
- MathSciNet review: 0551483