2 problems

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Multiplicity determined by the poset associated to a face of a Hibi toric variety
Multiplicity-poset conjecture. The multiplicity $\operatorname{mult}_{P_\tau}X(\mathcal{L})$ is determined by the poset $H(\tau)$ : whenever $\tau$ and $\tau'$ have isomorphic assoc…
Conjectureopenhibi-toric-varieties posets toric-varietiesarXiv posted 2 days ago
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Conjecture on multiplicative formulas for disconnected faces of Grassmann-Hibi toric varieties
Multiplicative-formula conjecture. There exists a multiplicative formula in $X_{d,n}$ similar to the known formula for a face that is a single suitable block, for a face that is a…
Conjectureopenhibi-toric-varieties multiplicity-theory toric-varietiesarXiv posted 2 days ago

Multiplicity determined by the poset associated to a face of a Hibi toric variety