平面曲线的格拉姆行列式
Gram determinant of planar curves
摘要：
本文研究了平面上曲线双线性型的Gram行列式，重点研究了带两个孔的圆盘。证明了基于$n-1$曲线的行列式整除基于$n$曲线的行列式。受基于圆盘中曲线和环中曲线的Gram行列式（分别为$A$型和$B$型Temperley-Lieb代数）的研究工作的启发，我们计算了基于双孔圆盘中曲线的Gram行列式的几个例子，并提出了Gram行列式的完全因子分解的一些理论.
英文摘要：
We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on $n-1$ curves divides the determinant based on $n$ curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an annulus (Temperley-Lieb algebra of type $A$ and $B$, respectively), we calculate several examples of the Gram determinant based on curves in a disk with two holes and advance conjectures on the complete factorization of Gram determinants.
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