AI 中文总结
本文引入有限quandle的子quandle滤过概念，通过对关联quandle着色箭图的子箭图进行 decategorification，定义两种多项式值纽结不变量，并与经典不变量比较以展示其区分能力。
AI 中文摘要
本文引入有限quandle的子quandle滤过概念，以此作为构造代数与组合纽结不变量的基础。子quandle的嵌套序列自然诱导出关联quandle着色箭图的子箭图滤过。通过对这些子箭图进行 decategorification，我们定义了两种新的多项式值纽结不变量：不尊重多项式和分级不尊重多项式，它们用于衡量所选quandle自同态集合对子quandle结构的尊重与不尊重程度。最后，我们将这些新工具与经典quandle计数不变量及箭图入度多项式进行比较，以说明其区分能力。
英文摘要
In this paper, we introduce the notion of subquandle filtrations for finite quandles as a foundation to construct algebraic and combinatorial link invariants. A nested sequence of subquandles naturally induces a filtration of the associated quandle coloring quiver by subquivers. By decategorifying these subquivers, we define two new polynomial-valued invariants of links: the disrespectful polynomial and the graded disrespectful polynomial, which measure how a chosen set of quandle endomorphisms respects and disrespects subquandle structure. Finally, we illustrate the distinguishing power of these new tools by comparing them to both classical quandle counting invariants and the quiver in-degree polynomial.
