Geodesic
Newton Complementary Duals of $f$-Ideals
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 231-241

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DOI

A 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.
DOI : 10.4153/S0008439518000024
Mots-clés : f-ideals, facet ideal, Stanley–Reisner correspondence, f-vectors, Newton complementary dual, Kruskal–Katona 
Budd, Samuel; Tuyl, Adam Van. Newton Complementary Duals of $f$-Ideals. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 231-241. doi: 10.4153/S0008439518000024
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     title = {Newton {Complementary} {Duals} of $f${-Ideals}},
     journal = {Canadian mathematical bulletin},
     pages = {231--241},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/S0008439518000024},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000024/}
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