AI 中文总结
本文建立了新的反对称化子-行列式恒等式，证明了Lukas Riegler等人的猜想，阐述了相关反对称化子，为解决Colomo与Pronko猜想提供了适配版本。
AI 中文摘要
断言反对称化子具有行列式表达式的恒等式，是多个交替符号矩阵计数公式证明的核心。反对称化子也频繁出现在对称函数理论中，例如Hall-Littlewood多项式可通过反对称化子实现。本文建立了这类恒等式中的一个新公式，从而证明了Lukas Riegler与其中一位作者的猜想；还阐述了一个相关的反对称化子，它可能对解决Colomo与Pronko的一个优美猜想起关键作用，并针对所提方法制定了该猜想的一个适配版本。
英文摘要
Identities asserting that an antisymmetrizer admits a determinantal expression are central to several proofs of counting formulas for alternating sign matrices. Antisymmetrizers appear also frequently in symmetric function theory as, for instance, the Hall-Littlewood polynomials can be realized via antisymmetrizers. In this paper, we establish a new identity of this type, thereby proving a conjecture of Lukas Riegler and one of the authors. We also elaborate on a related antisymmetrizer that may be pivotal in resolving a beautiful conjecture of Colomo and Pronko, and we formulate a version of their conjecture tailored to the suggested approach.
Comments16 pages
