Letzter, Shoham;
Sgueglia, Amedeo;
(2025)
On a problem of Brown, Erdős and Sós.
Proceedings of the American Mathematical Society
, 153
(7)
pp. 2729-2743.
10.1090/proc/16902.
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Abstract
Let f (r) (n; s, k) be the maximum number of edges in an n-vertex r-uniform hypergraph not containing a subhypergraph with k edges on at most s vertices. Recently, Delcourt and Postle, building on work of Glock, Joos, Kim, K¨uhn, Lichev and Pikhurko, proved that the limit limn→∞ n −2f (3)(n; k + 2, k) exists for all k ≥ 2, solving an old problem of Brown, Erd˝os and S´os (1973). Meanwhile, Shangguan and Tamo asked the more general question of determining if the limit limn→∞ n −tf (r) (n; k(r − t) + t, k) exists for all r > t ≥ 2 and k ≥ 2. Here we make progress on their question. For every even k, we determine the value of the limit when r is sufficiently large with respect to k and t. Moreover, we show that the limit exists for k ∈ {5, 7} and all r > t ≥ 2.
| Type: | Article |
|---|---|
| Title: | On a problem of Brown, Erdős and Sós |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/proc/16902 |
| Publisher version: | https://doi.org/10.1090/proc/16902 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10210437 |
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