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Published online by Cambridge University Press: 12 April 2016
A number of M giant stars with periods of the order of a few days were discovered by the Hipparcos mission. Similar stars may also have been found by other large-scale surveys. Parallaxes and colour indices of a sample of these stars were used to estimate their radii, temperatures and luminosities. It is shown that it is very unlikely that they are ellipsoidal or spotted variables, and that they are most likely pulsating in high overtone modes.