Geodesic
The covering lemma and q-analogues of extremal set theory problems
Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article no. 07, 13 p.

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We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to show how results concerning forbidden subposet problems in the Boolean poset imply analogous results in the poset of subspaces of a finite vector space. We also study generalized forbidden subposet problems in the poset of subspaces.
DOI : 10.26493/1855-3974.2677.b7f
Keywords: Subspace lattice, forbidden subposet, covering, profile polytope 
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Dániel Gerbner. The covering lemma and q-analogues of extremal set theory problems. Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article  no. 07, 13 p. doi : 10.26493/1855-3974.2677.b7f. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2677.b7f/

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