论文标题
Charney-Davis的猜想，用于简单的薄聚球员
The Charney-Davis conjecture for simple thin polyominoes
论文作者
论文摘要
令$ \ Mathcal {p} $为简单的薄polyomino，而$ \ bbbk $ a字段。令$ r $是与$ \ mathcal {p} $相关的to the coric $ \ bbbk $ -algebra。将$ r $的希尔伯特系列写入$ h_ {r}（t）/（1-t）^{\ dim（r）} $。我们表明$$（ - 1）^{\ left \ lfloor {\ frac {\ mathrm {deg} h_r（t）} {2}} {2}} \ right \ rfloor} h_ {r} h_ {r}（ - 1）\ geq 0 $ $ r $ r $ is gorerenstein。这表明与简单的薄聚元素相关的戈伦斯坦环满足了Charney-Davis的猜想。
Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algebra associated to $\mathcal{P}$. Write the Hilbert series of $R$ as $h_{R}(t)/(1-t)^{\dim(R)}$. We show that $$(-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.
