论文标题
与麦克唐纳多项式有关的某些共同介绍身份的射界证明
Bijective proofs of some coinversion identities related to Macdonald polynomials
论文作者
论文摘要
本文提供了艾耶，曼德尔什塔姆和马丁（Arxiv：2011.06117）最初发现的一些新型共同毒物身份的徒证明，这是他们证明修改后的麦克唐纳麦当劳多nomials $ \ tilde {h}_μ$ $ $的新组合公式的一部分。这些作者使用了$ q $ binmial系数的复杂代数操纵来证明这些身份，这意味着证明其公式满足表征$ \ tilde {h} _ $的公理所需的某些射击。他们提出了明确构建此类徒的开放问题。我们在这里解决这个问题。
This paper gives bijective proofs of some novel coinversion identities first discovered by Ayyer, Mandelshtam, and Martin (arxiv:2011.06117) as part of their proof of a new combinatorial formula for the modified Macdonald polynomials $\tilde{H}_μ$. Those authors used intricate algebraic manipulations of $q$-binomial coefficients to prove these identities, which imply the existence of certain bijections needed in their proof that their formula satisfies the axioms characterizing $\tilde{H}_μ$. They posed the open problem of constructing such bijections explicitly. We resolve that problem here.
