Generating functions for formal power series in noncommuting variables.
نویسندگان
چکیده
منابع مشابه
Symmetric Functions in Noncommuting Variables
Consider the algebra Q〈〈x1, x2, . . .〉〉 of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x1, x2, . . .) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In p...
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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: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1960-0118748-x