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A permutation based approach to the -deformation of the Dynkin Operator
Darij Grinberg, Ekaterina A. Vassilieva
Introduced by Solomon, the descent algebra is a significant subalgebra of the group algebra of the symmetric group related to many important algebraic and combinato…
The enriched -monomial basis of the quasisymmetric functions
Darij Grinberg, Ekaterina A. Vassilieva
We construct a new family of quasisymmetric functions for each element of the base ring. We call them the…
The left-to-right minima basis of the group algebra of the symmetric group (updated version)
Darij Grinberg, Ekaterina A. Vassilieva
We introduce a new basis of the group algebra of the symmetric group, built using the left-to-right minima sets of permutations. We show that on this basis, the descent algebra act…
Quasisymmetric expansion of Hall-Littlewood symmetric functions
Darij Grinberg, Ekaterina A. Vassilieva
In our previous works we introduced a -deformation of the generating functions for enriched -partitions. We call the evaluation of this generating functions on labelled chain…