POLYTOPAL REALIZATIONS OF FINITE TYPE g-VECTOR FANS
POLYTOPAL REALIZATIONS OF FINITE TYPE g-VECTOR FANS
复制标题
有限型g矢量风扇的多面体实现
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Salvatore Stella
中科院分区：
文献类型：
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作者：
Vincent Pilaud;Salvatore Stella
本文证明了对任意有限型初始交换矩阵B n，无论是非循环的还是非循环的，都存在一个广义结合面阿索（B n），它的法扇是主系数簇代数Apr（B n）的g-向量扇F（B n）.特别地，当在适当的方向上定向时，该广义协面体阿索（B）的图是Apr（B）的绿色突变的图。当B n是无环的，阿索（B n）符合以前已知的实现广义结合面体，通过删除不等式的方面描述的置换面体。我们表明，这方面的建设仍然是任何类型的A初始交换矩阵，但失去了一般任意有限类型。我们还证明了所有构造的广义结合面体的顶点重心都在原点。最后，我们的实现自然地导致构建一个通用的结合面体，同时包含所有的g-向量风扇F（B）的所有初始交换矩阵的一个给定的有限型。
This paper shows that for any finite type initial exchange matrix B◦, acyclic or not, there exists a generalized associahedron Asso(B◦) whose normal fan is the g-vector fan F(B◦) of the cluster algebra Apr(B◦) with principal coefficients. In particular, when oriented in a suitable direction, the graph of this generalized associahedron Asso(B◦) is the graph of green mutations of Apr(B◦). When B◦ is acyclic, Asso(B◦) coincides with previously known realizations of generalized associahedra, obtained by deleting inequalities in the facet description of the permutahedron. We show that this aspect of the construction remains for any type A initial exchange matrix, but is lost in general for arbitrary finite types. We also prove that the vertex barycenter of all constructed generalized associahedra is at the origin. Finally, our realizations naturally lead to construct a universal associahedron which simultaneously contains all g-vector fans F(B◦) for all initial exchanged matrix of a given finite type.
影响因子：
1.1
作者：
Ceballos, Cesar;Santos, Francisco;Ziegler, Guenter M.
通讯作者：
Ziegler, Guenter M.
DOI：
10.1090/s0002-9947-2014-06239-9
发表时间：
2013-01
期刊：
Discrete Mathematics & Theoretical Computer Science
影响因子：
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作者：
Cesar Ceballos;Vincent Pilaud
通讯作者：
Cesar Ceballos;Vincent Pilaud