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arXiv · 2607.07870

The Antipodes of $q$-Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions

Shaul Zemel
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Abstract

We prove the antipode formula for the $q$-deformations of quasi-symmetric functions. We also define a fundamental basis for non-commutative quasi-symmetric functions, and establish a partial antipode formula there. Our method also reduce to a new proof for the known antipode formula on the usual quasi-symmetric functions.

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Shaul Zemel. 2026-07-08. The Antipodes of $q$-Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions. https://arxiv.org/abs/2607.07870

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