Abstract
Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.
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Presented by J. Kung.
This research was supported by the NFSR of Hungary (OTKA), grant numbers K77432 and K83219, and by TÁMOP-4.2.1/B-09/1/KONV-2010-0005.
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Adaricheva, K., Czédli, G. Note on the description of join-distributive lattices by permutations. Algebra Univers. 72, 155–162 (2014). https://doi.org/10.1007/s00012-014-0295-y
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DOI: https://doi.org/10.1007/s00012-014-0295-y