论文标题
丰富的感谢您[\ vec {d}] $ - 分区
Enriched toric $[\vec{D}]$-partitions
论文作者
论文摘要
本文开发了丰富的感谢您[\ vec {d}] $ - 分区的理论。 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} $。在考虑丰富的$ p $ - 分区时，以与线性排列的峰值集相同的方式，环状排列的环状峰集在我们的理论中起着重要作用。基于此框架讨论了相关的多项式。
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.
