Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
نویسندگان
چکیده
منابع مشابه
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan [12]. The bases for this algebra are indexed by set partitions. We show that there exist a natural inclusion of the Hopf algebra of noncommutative symmetric functions studied in [17] in this larger space. We also consider this algebra a...
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In [12], Stanley associated with a graph G a symmetric function XG which reduces to G’s chromatic polynomial XG(n) under a certain specialization of variables. He then proved various theorems generalizing results about XG(n), as well as new ones that cannot be interpreted on the level of the chromatic polynomial. Unfortunately, XG does not satisfy a Deletion-Contraction Law which makes it diffi...
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Let Πn denote the set of all set partitions of {1, 2, . . . , n}. We consider two subsets of Πn, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let En ⊆ Πn be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, Tn−1. Given π ∈ Πm and σ ∈ Πn, define their slash product to be π|σ = π∪(σ+m)...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2008
ISSN: 1496-4279,0008-414X
DOI: 10.4153/cjm-2009-013-0