Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory
arXiv:1111.6258
Abstract
We construct an Eliahou-Kervaire-like minimal free resolution of the alternative polarization of a Borel fixed ideal . It yields new descriptions of the minimal free resolutions of itself and , where 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 is generated in one degree, our description is equivalent to that of Nagel and Reiner.
27 pages; examples and figures added; some errors corrected; to appear in J. Algebraic Combin