1 citations · 1 across the 7 of their papers we have counts for
7 papers
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…
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…
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…
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 "en…
The algebra of extended peaks
Darij Grinberg, Ekaterina A. Vassilieva
Building up on our previous works regarding -deformed -partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebra…
Bijective Enumeration of 3-Factorizations of an N-Cycle
E. A. Vassilieva
This paper is dedicated to the factorizations of the symmetric group. Introducing a new bijection for partitioned 3-cacti, we derive an el- egant formula for the number of factoriz…