{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LHSZNSHNZWCTAOVAWMULOJAJBF","short_pith_number":"pith:LHSZNSHN","schema_version":"1.0","canonical_sha256":"59e596c8edcd85303aa0b328b7240909553d23d87647652ce19df482f6def781","source":{"kind":"arxiv","id":"1805.07197","version":1},"attestation_state":"computed","paper":{"title":"Universality of vector sequences and universality of Tverberg partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Attila Por","submitted_at":"2018-05-18T13:26:50Z","abstract_excerpt":"A result of Rosenthal says that for every $q>1$ and $n \\in \\mathbb{N}$ there is $N \\in \\mathbb{N}$ such that every sequence of $N$ distinct positive numbers contains, after a suitable translation and possible multiplication by $-1$, a subsequence $a_1,\\ldots,a_n$ that is either $q$-increasing (that is, $a_{i+1}>qa_i$ for all $i$) or $1/q$-decreasing ($a_{i+1}1$ and $n \\in \\mathbb{N}$ there is $N \\in \\mathbb{N}$ such that every sequence of $N$ distinct positive numbers contains, after a suitable translation and possible multiplication by $-1$, a subsequence $a_1,\\ldots,a_n$ that is either $q$-increasing (that is, $a_{i+1}>qa_i$ for all $i$) or $1/q$-decreasing ($a_{i+1}