2022/08/31 by Jinting Liang, Liang, Jinting
Computer Science · Mathematics · #05A05 (Primary) 05E05 #06A11 (secondary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2209.00051
openalex publication_date 2022/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops the theory of enriched toric [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 QSym, our enriched toric [D]-partitions will generate the cyclic peak algebra which is a subring 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.