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arXiv · 2608.13544

Skew Hives, Skew Skeps, Skew Schur Log-Concavity

Tuong Le·Son Nguyen
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Abstract

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.

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Tuong Le, Son Nguyen. 2026-08-13. Skew Hives, Skew Skeps, Skew Schur Log-Concavity. https://arxiv.org/abs/2608.13544

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