When lattice cubes meet affine subspaces: a short note
L\^e Th\`anh D\~ung Nguy\^en
TL;DR
This paper provides concise proofs of well-known results regarding the intersection size of lattice cubes with affine subspaces and the minimal number of affine subspaces required to cover a lattice cube.
Contribution
It offers simplified, clear proofs of folklore results related to lattice cubes and affine subspaces, enhancing understanding and accessibility.
Findings
Maximum intersection size of lattice cube with an affine subspace
Minimum number of affine subspaces to cover a lattice cube
Simplified proofs of known folklore results
Abstract
We give short and simple proofs of what seem to be folklore results: * the maximum cardinality of the intersection of a lattice cube with an affine subspace; * the minimum number of affine subspaces needed to cover a lattice cube.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Advanced Algebra and Logic