Geodesic
On non-intersecting arithmetic progressions
Régis de la Bretèche 1   ; Kevin Ford 2   ; Joseph Vandehey 2
1 Institut de Mathématiques de Jussieu UMR 7586 Université Paris Diderot – Paris 7 UFR de Mathématiques, case 7012 Bâtiment Chevaleret 75205 Paris Cedex 13, France
2 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A.
Acta Arithmetica, Tome 157 (2013) no. 4, pp. 381-392 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than $x$. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about $\varDelta $-systems (also known as sunflowers).
DOI : 10.4064/aa157-4-5
Keywords: improve known bounds maximum number pairwise disjoint arithmetic progressions using distinct moduli close gap between upper lower bounds even further under assumption conjecture combinatorics about vardelta systems known sunflowers

Régis de la Bretèche  1   ; Kevin Ford  2   ; Joseph Vandehey  2

1 Institut de Mathématiques de Jussieu UMR 7586 Université Paris Diderot – Paris 7 UFR de Mathématiques, case 7012 Bâtiment Chevaleret 75205 Paris Cedex 13, France
2 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A. 
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Régis de la Bretèche; Kevin Ford; Joseph Vandehey. On non-intersecting arithmetic progressions. Acta Arithmetica, Tome 157 (2013) no. 4, pp. 381-392. doi: 10.4064/aa157-4-5

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