Newton Complementary Duals of -Ideals Academic Article uri icon

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abstract

  • AbstractA square-free monomial ideal$I$of$k[x_{1},\ldots ,x_{n}]$is said to be an$f$-ideal if the facet complex and non-face complex associated with$I$have the same$f$-vector. We show that$I$is an$f$-ideal if and only if its Newton complementary dual$\widehat{I}$is also an$f$-ideal. Because of this duality, previous results about some classes of$f$-ideals can be extended to a much larger class of$f$-ideals. An interesting by-product of our work is an alternative formulation of the Kruskal–Katona theorem for$f$-vectors of simplicial complexes.

publication date

  • June 2019