{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7BWVGZW2Y4B3GVPD7NNB4ZQOXZ","short_pith_number":"pith:7BWVGZW2","schema_version":"1.0","canonical_sha256":"f86d5366dac703b355e3fb5a1e660ebe721ed25525cde0034b6a40867c9d9292","source":{"kind":"arxiv","id":"1701.02762","version":1},"attestation_state":"computed","paper":{"title":"Small union with large set of centers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Tam\\'as Keleti","submitted_at":"2017-01-10T19:32:28Z","abstract_excerpt":"Let $T\\subset{\\mathbb R}^n$ be a fixed set. By a scaled copy of $T$ around $x\\in{\\mathbb R}^n$ we mean a set of the form $x+rT$ for some $r>0$.\n In this survey paper we study results about the following type of problems: How small can a set be if it contains a scaled copy of $T$ around every point of a set of given size? We will consider the cases when $T$ is circle or sphere centered at the origin, Cantor set in ${\\mathbb R}$, the boundary of a square centered at the origin, or more generally the $k$-skeleton ($0\\le k0$.\n In this survey paper we study results about the following type of problems: How small can a set be if it contains a scaled copy of $T$ around every point of a set of given size? We will consider the cases when $T$ is circle or sphere centered at the origin, Cantor set in ${\\mathbb R}$, the boundary of a square centered at the origin, or more generally the $k$-skeleton ($0\\le k