Abstract:We look at the number L(n) of O-sequences of length n. Recall that an Osequence can be defined algebraically as the Hilbert function of a standard graded k-algebra, or combinatorially as the f -vector of a multicomplex. The sequence L(n) was first investigated in a recent paper by commutative algebraists Enkosky and Stone, inspired by Huneke. In this note, we significantly improve both of their upper and lower bounds, by means of a very short partition-theoretic argument. In particular, it turns out that, for … Show more
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