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arXiv · 2209.00051

Enriched toric $[\vec{D}]$-partitions

Jinting Liang
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Abstract

This paper develops the theory of enriched toric $[\vec{D}]$-partitions. Whereas Stembridge's enriched $P$-partitions give rises to the peak algebra which is a subring of the ring of quasi-symmetric functions $\text{QSym}$, our enriched toric $[\vec{D}]$-partitions will generate the cyclic peak algebra which is a subring of cyclic quasi-symmetric functions $\text{cQSym}$. In the same manner as the peak set of linear permutations appears when considering enriched $P$-partitions, the cyclic peak set of cyclic permutations plays an important role in our theory. The associated order polynomial is discussed based on this framework.

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Jinting Liang. 2022-09-09. Enriched toric $[\vec{D}]$-partitions. https://arxiv.org/abs/2209.00051

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