论文标题
在对称边缘多面体的伽马载体上
On the gamma-vector of symmetric edge polytopes
论文作者
论文摘要
我们从确定性和概率的角度研究了与$ H^*$ - 对称边缘多型的向量相关的$γ$ - 向量。在确定性方面，我们证明任何图表的$γ_2$都不是$γ_2$，并且当$γ_2= 0 $时完全表征了情况。后者还证实了Lutz和Nevo在对称边缘多面体领域中的猜想。在概率方面，我们表明大多数Erdős-rényi随机图的对称边缘多型的$γ$ - 向量几乎肯定是毫无疑问的，直到任何固定条目。这证明了GAL的猜想在这种情况下几乎肯定是渐近的，肯定是任意的单型三角剖分。
We study $γ$-vectors associated with $h^*$-vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonnegativity of $γ_2$ for any graph and completely characterize the case when $γ_2 = 0$. The latter also confirms a conjecture by Lutz and Nevo in the realm of symmetric edge polytopes. On the probabilistic side, we show that the $γ$-vectors of symmetric edge polytopes of most Erdős-Rényi random graphs are asymptotically almost surely nonnegative up to any fixed entry. This proves that Gal's conjecture holds asymptotically almost surely for arbitrary unimodular triangulations in this setting.
