Abstract
Distributive lattices belong to the best studied ordered structures. A. Huhn introduced a generalisation of this lattice property, called n-distributivity. We present two new methods to recognise the parameter n of this property for a given structure. For this purpose we use the arrow relations in a formal context and implications with proper premise. Additionally, we consider subsets of an order relation ≤ on a finite set P with an additional property. These subsets will be called left clearings of ≤. We show that the family of left clearings forms a complete dually l-distributive lattice, where l denotes the length of (P, ≤ ). Using these results, we determine that parameter n for Tamari lattices for the n-distributivity and dually n-distributivity.
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References
Bennett, M.K., Birkhoff, G.: Two families of Newmann lattices. Algebra Universalis 32, 115–144 (1994)
Bergmann, G.M.: On lattices of convex sets in \(\mathbb R^n\). Algebra Universalis 53, 357–395 (2005)
Ganter, B., Wille, R.: FCA– Mathematical Foundations. Springer, Heidelberg (1999)
Geyer, W.: On Tamari lattices. Discrete Mathematics 133, 99–122 (1994)
Huhn, A.P.: Schwach distributive Verbände. I. Acta Sci. Math (Szeged) 33, 297–305 (1972)
Huhn, A.P.: On non-modular n-distributive lattices, I. Lattices of convex sets. Acta Sci. Math (Szeged) 52, 35–45 (1988)
Libkin, L.: n-distributivity, dimension and Carathéodory’s theorem. Algebra Universalis 34, 72–95 (1995)
Tamari, D.: The algebra of bracketings and their enumeration. Nieuw Arch. Wiskunde III. Ser. 10, 193–206 (1962)
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Reppe, H. (2007). An FCA Perspective on n-Distributivity. In: Priss, U., Polovina, S., Hill, R. (eds) Conceptual Structures: Knowledge Architectures for Smart Applications. ICCS 2007. Lecture Notes in Computer Science(), vol 4604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73681-3_19
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DOI: https://doi.org/10.1007/978-3-540-73681-3_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73680-6
Online ISBN: 978-3-540-73681-3
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