Alternative polarizations of Borel fixed ideals, EliahouKervaire type resolution and discrete Morse theory
We construct an EliahouKervaire-like minimal free resolution of the alternative polarization \(\operatorname{\mathsf{b-pol}}(I)\) of a Borel fixed ideal I. It yields new descriptions of the minimal free resolutions of I itself and I sq , where (?) sq is the squarefree operation in the shifting theory. These resolutions are cellular, and the (common) supporting cell complex is given by discrete Morse theory. If I is generated in one degree, our description is equivalent to that of Nagel and Reiner.
borel fixed ideal discrete morse theory squarefree strongly stable monomial ideal eliahoukervaire resolution