Record link: 
http://hdl.handle.net/20.500.12708/190575
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Title: 
Representing partition lattices through FCA
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Citation: 
Behrisch, M., Chavarri Villarello, A., & Vargas-García, E. (2021). Representing partition lattices through FCA. In A. Braud, A. Buzmakov, T. Hanika, & F. Le Ber (Eds.), Formal Concept Analysis: 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021, Proceedings (pp. 3–19). Springer. https://doi.org/10.1007/978-3-030-77867-5_1
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Publisher DOI: 
10.1007/978-3-030-77867-5_1
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Behrisch, Mike 
Chavarri Villarello, Alain 
Vargas-García, Edith 
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Organisational Unit: 
E104-01 - Forschungsbereich Algebra 
E104 - Institut für Diskrete Mathematik und Geometrie 
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Published in: 
Formal Concept Analysis: 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021, Proceedings 
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ISBN: 
978-3-030-77866-8
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Volume: 
12733
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DOI of the book: 
10.1007/978-3-030-77867-5
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Date (published): 
22-Jun-2021
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Event name: 
16th International Conference on Formal Concept Analysis (ICFCA 2021) 
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Event date: 
29-Jun-2021 - 2-Jul-2021
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Event place: 
Strasbourg, France
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Number of Pages: 
17
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Publisher: 
Springer, Cham
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Keywords: 
Integer partition; Join-irreducibility; Standard context; Context embedding
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Abstract: 
We investigate the standard context, denoted by 𝕂(𝓛ₙ), of the lattice 𝓛ₙ of partitions of a positive integer 𝑛 under the dominance order. Motivated by the discrete dynamical model to study integer partitions by Latapy and Duong Phan and by the characterization of the supremum and (infimum) irreducible partitions of 𝑛 by Brylawski, we show how to construct the join-irreducible elements of 𝓛ₙ₊₁ from 𝓛ₙ. We employ this construction to count the number of join-irreducible elements of 𝓛ₙ, and confirm that the number of objects (and attributes) of 𝕂(𝓛ₙ) has order 𝛩(𝑛²). We also discuss the embeddability of 𝕂(𝓛ₙ) into 𝕂(𝓛ₙ₊₁) with special emphasis on 𝑛 = 9.
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Research Areas: 
Mathematical and Algorithmic Foundations: 10%
Fundamental Mathematics Research: 90%
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Science Branch: 
1020 - Informatik: 10%
1010 - Mathematik: 90%
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