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arXiv · 2406.00581

On a Pieri-like rule for the Petrie symmetric functions

Emma Yu Jin·Naihuan Jing·Ning Liu
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Abstract

A $k$-ribbon tiling is a decomposition of a connected skew diagram into disjoint ribbons of size $k$. In this paper, we establish a connection between a subset of $k$-ribbon tilings and Petrie symmetric functions, thus providing a combinatorial interpretation for the coefficients in a Pieri-like rule for the Petrie symmetric functions due to Grinberg (Algebr. Comb. 5 (2022), no. 5, 947-1013). This also extends a result by Cheng, Chou and Eu et al. (Proc. Amer. Math. Soc. 151 (2023), no. 5, 1839-1854). As a bonus, our findings can be effectively utilized to derive certain specializations.

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Emma Yu Jin, Naihuan Jing, Ning Liu. 2024-06-02. On a Pieri-like rule for the Petrie symmetric functions. https://arxiv.org/abs/2406.00581

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