论文标题
通过最小矩阵乘法在整数排列上的扩展云量产品
An extended Demazure product on integer permutations via min-plus matrix multiplication
论文作者
论文摘要
Coxeter团体拥有一个协会操作，称为各种味，贪婪或$ 0 $ -HECKE产品。对于对称组，该产品在与排列相关的两个矩阵的最小（热带）半矩阵中具有有趣的表述为基质乘法。我们证明，这种最低公式的公式扩展到在更大的整数排列中提供纽唑的产品，包括所有变化的排列，这些排列会改变许多整数的有限迹象。我们证明了该产品的几种替代描述以及它的一些有用的属性。这些结果是为了在代数和热带曲线的Brill-Noether理论中提供未来应用的发展。该连接在附录中进行了调查。
Coxeter groups possess an associative operation, called variously the Demazure, greedy, or $0$-Hecke product. For symmetric groups, this product has an amusing formulation as matrix multiplication in the min-plus (tropical) semiring of two matrices associated to the permutations. We prove that this min-plus formulation extends to furnish a Demazure product on a much larger group of integer permutations, consisting of all permutations that change the sign of finite many integers. We prove several alternative descriptions of this product and some useful properties of it. These results were developed in service of future applications to Brill-Noether theory of algebraic and tropical curves; the connection is surveyed in an appendix.
