Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals (Q925311)

In the paper under review, the author studies the graded Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals. More precisely he proves that the graded Betti numbers of a strongy color-stable ideal are equal to those of some squarefree strongly color-stable ideal. In addition he gives an example to show that colored algebraic shifting, which was introduced by \textit{E. Babson} and \textit{I. Novik} [Electron. J. Comb. 11, No. 2, Research paper R25, 23 p. (2004-2005; Zbl 1085.52004)], does not always preserve the Betti numbers of balanced complexes.