The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Journal of Algebraic Combinatorics: An International Journal
European Journal of Combinatorics
A free subalgebra of the algebra of matroids
European Journal of Combinatorics
A unique factorization theorem for matroids
Journal of Combinatorial Theory Series A
Linear spaces, transversal polymatroids and ASL domains
Journal of Algebraic Combinatorics: An International Journal
A matroid-friendly basis for the quasisymmetric functions
Journal of Combinatorial Theory Series A
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To every subspace arrangement X we will associate symmetric functions 驴[X] and 驴[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They can be defined for discrete polymatroids as well. The invariant 驴[X] specializes to the Tutte polynomial ${\mathcal{T}}[\mathbf{X}]$ . Billera, Jia and Reiner recently introduced a quasi-symmetric function 驴[X] (for matroids) which behaves valuatively with respect to matroid base polytope decompositions. We will define a quasi-symmetric function ${\mathcal{G}}[\mathbf{X}]$ for polymatroids which has this property as well. Moreover, ${\mathcal{G}}[\mathbf{X}]$ specializes to 驴[X], 驴[X], ${\mathcal{T}}[\mathbf{X}]$ and 驴[X].