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In [Journal of Pure and Applied Algebra {224} (2020), no 12, 106449], V.Mazorchuk and R. Mr{\dj}en (with some help by A. Hultman) prove that, given aWeyl group, the intersection of a Bruhat interval with a parabolic coset has aunique maximal element and a unique minimal element. We show that suchintersections are actually Bruhat intervals also in the case of an arbitraryCoxeter group.

Bruhat intervals and parabolic cosets in arbitrary Coxeter groups