A distributive lattice connected with arithmetic progressions of length three
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/104774 https://orcid.org/0000-0003-3123-8241 |
| Summary: | 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. |
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