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

Liang, Jinting

doi:10.5802/alco.314

Enriched toric

[\vec{D}]

-partitions

Liang, Jinting ¹

¹ Michigan State University Department of Mathematics 619 Red Cedar Road C212 Wells Hall East Lansing MI 48824-1027 (USA)

Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1491-1518.

Abstract

This paper develops the theory of enriched toric $[\vec{D}]$ -partitions. Whereas Stembridge’s enriched $P$ -partitions give rise to the peak algebra which is a subring of the ring of quasi-symmetric functions $QSym$ , our enriched toric $[\vec{D}]$ -partitions generate the cyclic peak algebra which is a subring of the ring of cyclic quasi-symmetric functions $cQSym$ . 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.

Received: 2022-09-12
Accepted: 2023-05-01
Published online: 2024-01-08

DOI: 10.5802/alco.314

Classification: 05A05, 05E05, 06A11
Keywords: Cyclic peak, cyclic permutation, cyclic quasi-symmetric function, enriched $P$-partition, toric poset, order polynomial

Author's affiliations:

Liang, Jinting ¹

¹ Michigan State University Department of Mathematics 619 Red Cedar Road C212 Wells Hall East Lansing MI 48824-1027 (USA)

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Liang, Jinting. Enriched toric $[\vec{D}]$-partitions. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1491-1518. doi : 10.5802/alco.314. https://alco.centre-mersenne.org/articles/10.5802/alco.314/

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