Geodesic
A Sauer-Shelah-Perles lemma for lattices
Stijn Cambie ; Bogdan Chornomaz ; Zeev Dvir1 ; Yuval Filmus2 ; Shay Moran
1Princeton University
2Technion - Israel Institute of Technology
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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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.
DOI : 10.37236/9273
Classification : 06B05, 05D05

Stijn Cambie    ; Bogdan Chornomaz    ; Zeev Dvir  1   ; Yuval Filmus  2   ; Shay Moran 

1 Princeton University
2 Technion - Israel Institute of Technology 
@article{10_37236_9273,
     author = {Stijn Cambie and Bogdan Chornomaz and Zeev Dvir and Yuval Filmus and Shay Moran},
     title = {A {Sauer-Shelah-Perles} lemma for lattices},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9273},
     zbl = {1484.06018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9273/}
}
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Stijn Cambie; Bogdan Chornomaz; Zeev Dvir; Yuval Filmus; Shay Moran. A Sauer-Shelah-Perles lemma for lattices. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9273

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