Science and Mathematics Faculty Publications

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 (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.

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