P -Partitions and Quasisymmetric Power Sums
P -Partitions and Quasisymmetric Power Sums
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P 分区和拟对称幂和
DOI：
10.1093/imrn/rnz375
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发表时间：
2020
影响因子：
1
通讯作者：
Weselcouch, Michael
中科院分区：
文献类型：
--
作者：
Liu, Ricky Ini;Weselcouch, Michael
标号命题的分划生成函数是一个拟对称函数，它列举了从到的保序映射。我们研究了这种生成函数在最近推出的1型拟对称幂和基上的展开。使用这种扩展，我们表明，连接，自然标记偏序集有不可约划分生成函数。我们还证明了串并联偏序集是由其划分生成函数唯一确定的。最后，我们给出了一个组合解释的系数的扩展的分区生成函数类似于Murnaghan-中山规则。
The-partition generating functionof a labeled posetis a quasisymmetric function enumerating certain order-preserving maps fromto. We study the expansion of this generating function in the recently introduced type 1 quasisymmetric power sum basis. Using this expansion, we show that connected, naturally labeled posets have irreducible-partition generating functions. We also show that series-parallel posets are uniquely determined by their partition generating functions. We conclude by giving a combinatorial interpretation for the coefficients of the-expansion of the-partition generating function akin to the Murnaghan–Nakayama rule.