Pregled bibliografske jedinice broj: 1252719
Another Note on Intervals in the Hales–Jewett Theorem
Another Note on Intervals in the Hales–Jewett Theorem // The Electronic Journal of Combinatorics, 29 (2022), 1; 62, 18 doi:10.37236/9400 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 1252719 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
Another Note on Intervals in the Hales–Jewett Theorem
Autori
Kamčev, Nina ; Spiegel, Christoph
Izvornik
The Electronic Journal of Combinatorics (1077-8926) 29
(2022), 1;
62, 18
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Hales-Jewett theorem
Sažetak
The Hales-Jewett Theorem states that any r-colouring of [m](n) contains a monochromatic combinatorial line if n is large enough. Shelah's proof of the theorem implies that for m = 3 there always exists a monochromatic combinatorial line whose set of active coordinates is the union of at most r intervals. For odd r, Conlon and Kamcev constructed r-colourings for which it cannot be fewer than r intervals. However, we show that for even r and large n, any r-colouring of [3](n) contains a monochromatic combinatorial line whose set of active coordinates is the union of at most r -1 intervals. This is optimal and extends a result of Leader and Ray for r = 2.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
