AI 中文总结
该研究引入斜蜂巢与斜筐模型，证明推广Lam等人猜想的斜舒尔对数凹性结果，获Newell-Littlewood数等的对数凹性结论，并解答Speyer关于相关组合结构双射的问题。
AI 中文摘要
Knutson和Tao的蜂巢是计算Littlewood-Richardson系数的组合模型。类似蜂巢，Speyer引入了skep（筐）并用以证明Lam-Postnikov-Pylyavskyy的舒尔对数凹性猜想。我们首先引入斜蜂巢（skew hive）与斜筐（skew skep）模型，二者可退化到蜂巢与筐，并用其证明推广Lam-Postnikov-Pylyavskyy猜想的斜舒尔对数凹性结果。作为推论，我们得到关于Newell-Littlewood数和影子斜舒尔函数的若干对数凹性结果。最后，我们阐明Nguyen-Nguyen-Woodruff给出的（斜）蜂巢、（斜）筐与可剥离表aux（表格）间的双射，解答了Speyer的问题。
英文摘要
Knutson and Tao's hives is a combinatorial model to compute Littlewood--Richardson coefficients. Similar to hives, Speyer introduced skeps and used them to prove a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy. We first introduce skew hive and skew skep models, which specialize to both hives and skeps, and use this to prove a skew Schur log-concavity result generalizing Lam--Postnikov--Pylyavskyy conjecture. As a consequence, we obtain some log-concavity results concerning Newell--Littlewood numbers and shadow skew Schur functions. Finally, we explain bijections between (skew) hives, (skew) skeps, and peelable tableaux by Nguyen--Nguyen--Woodruff, answering Speyer's question.
Comments26 pages, 5 figures, comments welcome!
