Geodesic
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, Tome 6 (2023) no. 6, pp. 1491-1518

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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.

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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)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Liang, Jinting. Enriched toric $[\vec{D}]$-partitions. Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1491-1518. doi: 10.5802/alco.314

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