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Abstract: The face numbers of simplicial complexes without missing faces of dimensionlarger than $i$ are studied. It is shown that among all such$d-1$-dimensional complexes with non-vanishing top homology, a certainpolytopal sphere has the componentwise minimal $f$-vector; and moreover, amongall such 2-Cohen-Macaulay 2-CM complexes, the same sphere has thecomponentwise minimal $h$-vector. It is also verified that the $l$-skeleton ofa flag $d-1$-dimensional 2-CM complex is $2d-l$-CM while the $l$-skeletonof a flag PL $d-1$-sphere is $2d-l$-homotopy CM. In addition, tight lowerbounds on the face numbers of 2-CM balanced complexes in terms of theirdimension and the number of vertices are established.



Autor: Michael Goff, Steven Klee, Isabella Novik

Fuente: https://arxiv.org/







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