Geodesic
Piecewise lexsegment ideals in exterior algebras
Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 287-307

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The problem of describing the Hilbert functions of homogeneous ideals of an exterior algebra over a field containing a fixed monomial ideal $I$ is considered. For this purpose the notion of a piecewise lexsegment ideal in an exterior algebra is introduced generalizing the notion of a lexsegment ideal. It is proved that if $I$ is a piecewise lexsegment ideal, then it is possible to describe the Hilbert functions of the homogeneous ideals containing $I$ in a way similar to that suggested by Kruskal and Katona for the situation $I=0$. Moreover, a generalization of the extremal properties of lexsegment ideals is obtained (the inequality for the Betti numbers). 
@article{SM_2005_196_2_a6,
     author = {D. A. Shakin},
     title = {Piecewise lexsegment ideals in exterior algebras},
     journal = {Sbornik. Mathematics},
     pages = {287--307},
     publisher = {mathdoc},
     volume = {196},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_2_a6/}
}
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D. A. Shakin. Piecewise lexsegment ideals in exterior algebras. Sbornik. Mathematics, Tome 196 (2005) no. 2, pp. 287-307. http://geodesic.mathdoc.fr/item/SM_2005_196_2_a6/