Abstract
In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure balanced complex which shows that colored algebraic shifting, which was introduced by Babson and Novik, does not always preserve the dimension of reduced homology groups of balanced simplicial complexes.
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The author is supported by JSPS Research Fellowships for Young Scientists.
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Murai, S. Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals. J Algebr Comb 27, 383–398 (2008). https://doi.org/10.1007/s10801-007-0095-y
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DOI: https://doi.org/10.1007/s10801-007-0095-y