Related papers: The Colored Eulerian Descent Algebra
We propose a unified approach to prove general formulas for the joint distribution of an Eulerian and a Mahonian statistic over a set of colored permutations by specializing Poirier's colored quasisymmetric functions. We apply this method…
The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…
We introduce a unital associative algebra A over degenerate CP^1. We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions. Thereby we can regard A as a smooth degeneration limit of the…
We investigate color Lie rings over finite group algebras and their universal enveloping algebras. We exhibit these universal enveloping algebras as PBW deformations of skew group algebras: Every color Lie ring over a finite group algebra…
For a quasi-projective smooth geometrically integral variety over a number field $k$, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an…
The representations of various color Lie superalgebras by Hilbert series are the main topic of this work. The Color Lie superalgebras appear in various branches of mathematics (e.g., topology, algebraic groups, etc.). They are generalized…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-${\mathbb{Z}}$-module ${\mathcal{D}}_A(W)$ of the group algebra ${\mathbb{Z}} W$. We provide examples where this submodule is a subalgebra. This…
We define new statistics, (c, d)-descents, on the colored permutation groups Z_r \wr S_n and compute the distribution of these statistics on the elements in these groups. We use some combinatorial approaches, recurrences, and generating…
We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of…
For a commutative ring $R$ with identity, a Specker $R$-algebra is a commutative unital $R$-algebra generated by a Boolean algebra of idempotents, each nonzero element of which is faithful. Such algebras have arisen in the study of…
Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and Williams on the face enumeration of generalized permutohedra. They are $\gamma$-positive (in particular, palindromic and unimodal) polynomials which can be…
This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we…
In a recent paper, Regev and Roichman introduced the <_L order and the L-descent number statistic, des_L, on the group of colored permutations, C_a \wr S_n. Here we define the L-reverse major index statistic, rmaj_L, on the same group and…
In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using a Brauer graph…
We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…
A classic result of representation theory is Brauer's construction of a diagrammatical (geometrical) algebra whose matrix representation is a certain given matrix algebra, which is the commutating algebra of the enveloping algebra of the…