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A Distributive Lattice Connected with Arithmetic Progressions of Length Three by Liu, Fu; Stanley, Richard P. is a scholarly article available to read on EtoBox.

What is A Distributive Lattice Connected with Arithmetic Progressions of Length Three about?

Let $\mathcal{T}$ be a collection of 3-element subsets $S$ of $\{1, \ldots,n\}$ with the property that if $i<j<k$ and $a<b<c$ are two 3-element subsets in $S$, then there exists an integer sequence $x_1 < x_2 < \cdots < x_n$ such that $x_i, x_j, x_k$ and $x_a, x_b, x_c$ are arithmetic progressions. We determine the number of such collections $\mathcal{T}$ and the number of them of maximum size. These results confirm two conjectures of Noam Elkies.

Author

Liu, Fu; Stanley, Richard P.

Published

2013

Language

EN