The Implication Logic of (n, k)-Extremal Lattices View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017

AUTHORS

Alexandre Albano

ABSTRACT

We characterize the canonical bases of lattices which attain the upper bound in Sauer-Shelah’s lemma, i.e., the (n, k)-extremal lattices of [AC15]. A characteristic construction of such bases is presented. We make the case that this approach sheds light on important combinatorial properties. In particular, we give an explicit description of an (n, k)-extremal lattice with precisely \({n \atopwithdelims ()k-1} +k-2\) meet-irreducibles, together with its canonical basis and Whitney numbers. More... »

PAGES

39-55

Book

TITLE

Formal Concept Analysis

ISBN

978-3-319-59270-1
978-3-319-59271-8

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-59271-8_3

DOI

http://dx.doi.org/10.1007/978-3-319-59271-8_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1086117255


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