Skew Hives, Skew Skeps, Skew Schur Log-Concavity

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.