We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type $\tilde{C}$, namely, the two-boundary Temperley-Lieb algebra and the symplectic blob algebra. We provide a monomial basis for both algebras. The elements of these bases are parameterized by certain subsets of fully commutative elements. We enumerate these elements according to their affine length.

中文翻译：

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类型 $\stackrel{〜}{C}$ Temperley-Lieb代数商和加泰罗尼亚语组合数学

我们研究了作为类型的Temperley-Lieb代数的商出现的两个代数的一些代数和组合特征 $\stackrel{〜}{C}$，即两边界的Temperley-Lieb代数和辛Blob代数。我们为两个代数提供了单项式基础。这些基数的元素由完全可交换元素的某些子集参数化。我们根据它们的仿射长度来枚举这些元素。