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On Complete Symmetric Functions
SIAM Journal on Mathematical Analysis, 1988This paper is devoted to the study of properties of complete symmetric functions playing an important role in the theory of partitions and in combinatorics. Especially the representation and recursive formulas and inequalities involving functions in question are given. The theory is accompanied by some applications.
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On MacDonald's Symmetric Functions
Bulletin of the London Mathematical Society, 1992An algorithm for computing Macdonald's two-parameter symmetric functions is suggested. A transition matrix from the basis of power sums to the basis of Macdonald's functions is constructed recursively (with respect to the dominance partial order on partitions) by a method analogous to Shoji's method of computing the Green functions of \(\text{GL}(n,q)\)
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α-Chromatic Symmetric Functions
International Mathematics Research NoticesAbstract In this paper, we introduce the $\alpha $-chromatic symmetric functions $\chi ^{(\alpha )}_\pi [X;q]$, extending Shareshian and Wachs’ chromatic symmetric functions with an additional real parameter $\alpha $. We present positive combinatorial formulas with explicit interpretations.
Haglund, Jim, Oh, Jaeseong, Yoo, Meesue
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Decomposable Skew-Symmetric Functions
Moscow Mathematical Journal, 2003Summary: A skew-symmetric function \(F\) in several variables is said to be decomposable if it can be represented as a determinant det\((f_i(x_j))\) where \(f_i\) are univariate functions. We give a criterion of the decomposability in terms of a Plücker-type identity imposed on the function \(F\).
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