42,571 research outputs found
h-vectors of Gorenstein* simplicial posets
As is well known, h-vectors of simple (or simplicial) convex polytopes are
characterized. In fact, those h-vectors must satisfy Dehn-Sommerville equations
and some other inequalities. Simple convex polytopes determine Gorenstein*
simplicial posets and h-vectors are defined for simplicial posets. It is known
that h-vectors of Gorenstein* simplicial posets must satisfy Dehn-Sommerville
equations and that every component in the h-vectors must be non-negative. In
this paper we will show that h-vectors of Gorenstein* simplicial posets must
satisfy one more subtle condition conjectured by R. Stanley and complete
characterization of those h-vectors. Our proof is purely algebraic but the idea
of the proof stems from topology.Comment: 12 page
Normalized Weyl-type -product on K\"ahler manifolds
We define a normalized Weyl-type -product on general K\"{a}hler
manifolds. Expanding this product perturbatively we show that the cumbersome
term, which appears in a Berezin-type product, does not appear at least in the
first order of . This means a normalization factor, which is introduced
by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our
Weyl-type product at that order.Comment: to be published in Mod. Phys. Lett.
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