TY - JOUR A1 - Kamčev, Nina A1 - Spiegel, Christoph T1 - Another note on intervals in the Hales-Jewett theorem JF - Electronic Journal of Combinatorics N2 - 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 Kamčev 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 Räty for r=2. Y1 - 2022 U6 - https://doi.org/10.37236/6730 VL - 29 IS - 1 SP - P1.62 ER -