Trivial Meet and Join Within the Lattice of Monotone TrianglesThe Electronic Journal of Combinatorics
- Monotone triangle,
- alternating sign matrix,
AbstractThe 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.
Citation InformationAdam 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/