A sauer–shelah–perles lemma for lattices

Stijn Cambie; Bogdan Chornomaz; Zeev Dvir; Yuval Filmus; Shay Moran

doi:10.37236/9273

A sauer–shelah–perles lemma for lattices

Stijn Cambie, Bogdan Chornomaz, Zeev Dvir, Yuval Filmus, Shay Moran

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2 Scopus citations

Abstract

We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.

Original language	English
Article number	P4.19
Pages (from-to)	1-21
Number of pages	21
Journal	Electronic Journal of Combinatorics
Volume	27
Issue number	4
DOIs	https://doi.org/10.37236/9273
State	Published - 2020

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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title = "A sauer–shelah–perles lemma for lattices",

abstract = "We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.",

author = "Stijn Cambie and Bogdan Chornomaz and Zeev Dvir and Yuval Filmus and Shay Moran",

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AU - Cambie, Stijn

AU - Chornomaz, Bogdan

AU - Dvir, Zeev

AU - Filmus, Yuval

AU - Moran, Shay

N1 - Publisher Copyright: © The authors.

PY - 2020

Y1 - 2020

N2 - We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.

AB - We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.

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AN - SCOPUS:85095406966

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JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 4

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A sauer–shelah–perles lemma for lattices

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