Charles Darwin University

output

20042025

most citedUnmanned Aerial Vehicles in Smart Agriculture: Applications, Requirements and Challenges

612 citations

Showing math.COShow all

6 papers · 1 filter

math.CO2023★ 1 cited

Sizes of flat maximal antichains of subsets

Jerrold R. Griggs, Thomas Kalinowski, Uwe Leck +2

This is the second of two papers investigating for which positive integers $m$ there exists a maximal antichain of size $m$ in the Boolean lattice $B_{n}$ (the power set of $[n]:=\{1…

math.CO2021★ 6 cited

The saturation spectrum for antichains of subsets

Jerrold R. Griggs, Thomas Kalinowski, Uwe Leck +2

Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a maximal antichain of size $m$ in the Boolean lattice $B_{n}$ , that is, the power s…

math.CO2017★ 2 cited

Minimum Weight Flat Antichains of Subsets

Jerrold R. Griggs, Sven Hartmann, Thomas Kalinowski +2

Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains $F$ in the Boolean lattice $B_{n}$ of all subsets of $[n] := {1, 2, \dots, n}$ , where $\…

math.CO2012

Minimizing the regularity of maximal regular antichains of 2- and 3-sets

Thomas Kalinowski, Uwe Leck, Christian Reiher +1

Let $n ⩾ 3$ be a natural number. We study the problem to find the smallest $r$ such that there is a family $A$ of 2-subsets and 3-subsets of $[n] = {1, 2, ..., n}$ wi…

math.CO2012

Maximal antichains of minimum size

Thomas Kalinowski, Uwe Leck, Ian T. Roberts

Let $n ⩾ 4$ be a natural number, and let $K$ be a set $K \subseteq [n] := 1, 2, ..., n$ . We study the problem to find the smallest possible size of a maximal family $\mathcal{A}…

math.CO2009

On the number of Latin squares

Brendan D. McKay, Ian M. Wanless

We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order~11, (2) answer some questions of Alter by sho…