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Abstract: A new Z-basis for the space of quasisymmetric functions QSym, for short ispresented. It is shown to have nonnegative structure constants, and severalinteresting properties relative to the space of quasisymmetric functionsassociated to matroids by the Hopf algebra morphism F of Billera, Jia, andReiner. In particular, for loopless matroids, this basis reflects the gradingby matroid rank, as well as by the size of the ground set. It is shown that themorphism F is injective on the set of rank two matroids, and thatdecomposability of the quasisymmetric function of a rank two matroid mirrorsthe decomposability of its base polytope. An affirmative answer is given to theHilbert basis question raised by Billera, Jia, and Reiner.



Autor: Kurt W. Luoto

Fuente: https://arxiv.org/







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