ALGEBRAIC COMBINATORICS

no. 6
Enriched toric [D →]-partitions
Liang, Jinting1
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.

This paper develops the theory of enriched toric [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 [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:
Accepted:
Published online:
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
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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