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{\bf Eric Babson and Isabella Novik}
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{\bf Face Numbers and Nongeneric Initial Ideals}
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Certain necessary conditions on the face numbers and Betti numbers of
simplicial complexes endowed with a proper action of a prime order
cyclic group are established. A notion of colored algebraic shifting
is defined and its properties are studied. As an application a new
simple proof of the characterization of the flag face numbers of
balanced Cohen-Macaulay complexes originally due to Stanley
(necessity) and Bj\"orner, Frankl, and Stanley (sufficiency) is
given. The necessity portion of their result is generalized to certain
conditions on the face numbers and Betti numbers of balanced Buchsbaum
complexes.
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