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{\bf Uwe Nagel and Victor Reiner}
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{\bf Betti Numbers of Monomial Ideals and Shifted Skew Shapes}
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We present two new problems on lower bounds for Betti numbers of the
minimal free resolution for monomial ideals generated in a fixed
degree. The first concerns any such ideal and bounds the total Betti
numbers, while the second concerns ideals that are quadratic and
bihomogeneous with respect to two variable sets, but gives a more
finely graded lower bound.

These problems are solved for certain classes of ideals that
generalize (in two different directions) the edge ideals of
threshold graphs and Ferrers graphs.  In the process,  we produce
particularly simple cellular linear resolutions for strongly stable
and squarefree strongly stable ideals generated in a fixed degree,
and combinatorial interpretations for the Betti numbers of other
classes of ideals, all of which are independent of the coefficient
field.

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