Trivial Meet and Join Within the Lattice of Monotone Triangles

Authors

Adam J. Hammett, Cedarville UniversityFollow
John Engbers

Document Type

Article

Publication Date

2014

Journal Title

The Electronic Journal of Combinatorics

Volume

21

Issue

3

First Page

1

Last Page

15

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 infimumτ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 asn→ ∞. 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.

Keywords

Monotone triangle, alternating sign matrix, meet, join

Comments

© The Authors, 2014.

Recommended Citation

Hammett, Adam J. and Engbers, John, "Trivial Meet and Join Within the Lattice of Monotone Triangles" (2014). Science and Mathematics Faculty Publications. 318.
https://digitalcommons.cedarville.edu/science_and_mathematics_publications/318