论文标题
特斯勒多面体的变形锥
Deformation cone of Tesler polytopes
论文作者
论文摘要
对于$ \ boldsymbol {a} \ in \ r _ {\ geq 0}^{n} $，tesler polytope $ \ tes_ {n}（\ boldsymbol {a}）$是一组不含上三角形入口的上三角形矩阵，其挂钩总和是$ $ $ $ \ ba。我们首先给出了一个已知事实的不同证明，即每一个固定的$ \ boldsymbol {a} _ {0} \ in \ mathbb {r} _ {> 0}^{n} $，所有tesler polytopes $ \ tes_ {n}（n}（n}） $ \ tes_ {n}（\ boldsymbol {a} _ {0}）$。然后，我们计算$ \ tes_ {n}（\ boldsymbol {a} _ {0}）$的变形锥。在此过程中，我们还表明，$ \ tes_ {n}（\ boldsymbol {a} _ {0}）$的任何变形都是tesler polytope的翻译。最后，我们考虑了一个较大的称为流程多型的多型家族，其中包含tesler多型家族，并给出一个表征，在该系列中，流层是$ \ tes_ {n}的变形（\ boldsymbol {a} _ {0}）$。
For $\boldsymbol{a} \in \R_{\geq 0}^{n}$, the Tesler polytope $\tes_{n}(\boldsymbol{a})$ is the set of upper triangular matrices with non-negative entries whose hook sum vector is $\ba$. We first give a different proof of the known fact that for every fixed $\boldsymbol{a}_{0} \in \mathbb{R}_{>0}^{n}$, all the Tesler polytopes $\tes_{n}(\boldsymbol{a})$ are deformations of $\tes_{n}(\boldsymbol{a}_{0})$. We then calculate the deformation cone of $\tes_{n}(\boldsymbol{a}_{0})$. In the process, we also show that any deformation of $\tes_{n}(\boldsymbol{a}_{0})$ is a translation of a Tesler polytope. Lastly, we consider a larger family of polytopes called flow polytopes which contains the family of Tesler polytopes and give a characterization on which flow polytopes are deformations of $\tes_{n}(\boldsymbol{a}_{0})$.
