Trivial Meet and Join within the Lattice of Monotone Triangles

Authors

John Engbers, Marquette UniversityFollow
Adam Hammett, Bethel College - MishawakaFollow

Document Type

Article

Language

eng

Format of Original

1 p.

Publication Date

2014

Publisher

Electronic Journal of Combinatorics

Source Publication

Electronic Journal of Combinatorics

Source ISSN

1077-8926

Abstract

The lattice of monotone triangles (�_n, ≼) ordered by entry-wise comparisons is studied. Let τ_min denote the unique minimal element in this lattice, and τ_max the unique maximum. The number of r-tuples of monotone triangles (τ₁...,τ_r) with minimul infimum τ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 as n→ ∞. Thus, with high probability this even implies that one of the τ_i is τ_min (τ_max, resp.). Higher-order error terms are also discussed.

Comments

Published version. Electronic Journal of Combinatorics, Vol. 21, No. 3 (2014). Permalink. © 2014 The Authors. Used with permission.

Recommended Citation

Engbers, John and Hammett, Adam, "Trivial Meet and Join within the Lattice of Monotone Triangles" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 221.
https://epublications.marquette.edu/mscs_fac/221