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Article
Trivial Meet and Join Within the Lattice of Monotone Triangles
The Electronic Journal of Combinatorics
  • Adam J. Hammett, Cedarville University
  • John Engbers
Document Type
Article
Publication Date
1-1-2014
Abstract
The lattice of monotone triangles (𝕸n, ≼) ordered by entry-wise comparisons is studied. Let τmin denote the unique minimal element in this lattice, and τmax the unique maximum. The number of r-tuples of monotone triangles (τ1...,τr) with minimul infimumτmin (maximul supremum τmax, resp.) is shown to asymptotically approach r|𝕸n|r-1 asn→ ∞. Thus, with high probability this even implies that one of the τi is τmin (τmax, resp.). Higher-order error terms are also discussed.
Keywords
  • Monotone triangle,
  • alternating sign matrix,
  • meet,
  • join
Comments

© The Authors, 2014.

Citation Information
Adam J. Hammett and John Engbers. "Trivial Meet and Join Within the Lattice of Monotone Triangles" The Electronic Journal of Combinatorics Vol. 21 Iss. 3 (2014) p. 1 - 15
Available at: http://works.bepress.com/adam_hammett/9/