A distributive lattice connected with arithmetic progressions of length three

Author(s)
Liu, Fu; Stanley, Richard P
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Abstract
Let T be a collection of 3-element subsets S of {1,…,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[subscript 1]<x[subscript 2]<⋯<x[subscript n] such that x[subscript i],x[subscript j],x[subscript k] and x[subscript a],x[subscript b],x[subscript c] are arithmetic progressions. We determine the number of such collections T and the number of them of maximum size. These results confirm two conjectures of Noam Elkies.
Date issued
2014-10
URI
http://hdl.handle.net/1721.1/104774
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
The Ramanujan Journal
Publisher
Springer US
Citation
Liu, Fu, and Richard P. Stanley. “A Distributive Lattice Connected with Arithmetic Progressions of Length Three.” The Ramanujan Journal 36.1–2 (2015): 203–226.
Version: Author's final manuscript
ISSN
1382-4090
1572-9303
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