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The Charney-Davis conjecture for simple thin polyominoes
- Source :
- Communications in Algebra. 51:1654-1662
- Publication Year :
- 2022
- Publisher :
- Informa UK Limited, 2022.
-
Abstract
- Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algebra associated to $\mathcal{P}$. Write the Hilbert series of $R$ as $h_{R}(t)/(1-t)^{\dim(R)}$. We show that $$(-1)^{\left\lfloor{\frac{\mathrm{deg} h_R(t)}{2}}\right\rfloor}h_{R}(-1) \geq 0$$ if $R$ is Gorenstein. This shows that the Gorenstein rings associated to simple thin polyominoes satisfy the Charney-Davis conjecture.<br />Comment: To appear in Communications in Algebra
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 51
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....f793b5124f1a545b5d455af20ee68a36