Unions of intervals in codes based on powers of sets
| Autor: | Karam, Thomas |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that for every integer $d \ge 2$ there exists a dense collection of subsets of $[n]^d$ such that no two of them have a symmetric difference that may be written as the $d$th power of a union of at most $\lfloor d/2 \rfloor$ intervals. This provides a limitation on reasonable tightenings of a question of Alon from 2023 and of a conjecture of Gowers from 2009, and investigates a direction analogous to that of recent works of Conlon, Kam\v{c}ev, Leader, R\"aty and Spiegel on intervals in the Hales-Jewett theorem. Comment: 13 pages, submitted |
| Databáze: | arXiv |
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