Polytopes of roots of type AN
Polytopes of roots of type AN
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AN型根的多胞体
DOI：
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发表时间：
1999
影响因子：
0.7
通讯作者：
Soojin Cho
中科院分区：
文献类型：
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作者：
Soojin Cho
研究了 An−1 型根的多胞形，我们称之为 Pn。正根和原点的多胞形 已被考虑与数学的其他分支相关[4]。我们证明恰好 n 个副本形成了 Pn 的不相交覆盖。而且，这n个拷贝可以通过让n循环生成的对称群Sn的子群的元素作用于 来获得。我们还描述了 Pn 的面和 的一些方面，我们认为这在某些优化问题中很有用。作为副产品，我们获得了关于格路径数量的有趣恒等式以及两个单纯形乘积的三角剖分。
Polytopes of roots of type An−1 are investigated, which we call Pn. The polytopes, , of positive roots and the origin have been considered in relation to other branches of mathematics [4]. We show that exactly n copies of forms a disjoint cover of Pn. Moreover, those n copies of can be obtained by letting the elements of a subgroup of the symmetric group Sn generated by an n-cycle act on . We also characterise the faces of Pn and some facets of , which we believe to be useful in some optimisation problems. As by-products, we obtain an interesting identity on the number of lattice paths and a triangulation of the product of two simplices.