Alternative polarizations of Borel fixed ideals
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AbstractFor a monomial idealIof a polynomial ringS, apolarizationofIis a square-free monomial idealJof a larger polynomial ringsuch thatS/Iis a quotient of/Jby a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sendsours sends it tox1y2y3Using this idea, we recover/refine the results onsquare-free operationin the shifting theory of simplicial complexes. The present paper generalizes a result of Nagel and Reiner, although our approach is very different.
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2011 ◽
Vol 48
(2)
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pp. 220-226
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2019 ◽
Vol 19
(10)
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pp. 2050201
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2010 ◽
Vol 149
(2)
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pp. 229-246
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2016 ◽
Vol 16
(07)
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pp. 1750122
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