Related papers: Actions and identities on set partitions

A q-series with nonnegative power series coefficients is called positive. The partition statistics BG-rank is defined as an alternating sum of parities of parts of a partition. It is known that the generating function for the number of…

Given a representation of a finite group $G$ over some commutative base ring $\mathbf{k}$, the cofixed space is the largest quotient of the representation on which the group acts trivially. If $G$ acts by $\mathbf{k}$-algebra automorphisms,…

We present a categorification of the non-crossing partitions given by crystallographic Coxeter groups. This involves a category of certain bilinear lattices, which are essentially determined by a symmetrisable generalised Cartan matrix…

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be…

The usual, or type A_n, Tamari lattice is a partial order on T_n^A, the triangulations of an (n+3)-gon. We define a partial order on T_n^B, the set of centrally symmetric triangulations of a (2n+2)-gon. We show that it is a lattice, and…

Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through…

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

We introduce and study s-lecture hall P-partitions which is a generalization of s-lecture hall partitions to labeled (weighted) posets. We provide generating function identities for s-lecture hall P-partitions that generalize identities…

Let $\Gamma$ be a countable group. A $\Gamma$-action on a compact abelian group $X$ by continuous automorphisms of $X$ is called Noetherian if the dual of $X$ is Noetherian as a ${\mathbb Z}(\Gamma)$-module. We prove that any Noetherian…

We introduce an order on the set of non-divisorial ideals of a numerical semigroup $S$, and link antichains of this order with the star operations on $S$; subsequently, we use this order to find estimates on the number of star operations on…

Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids

Given a partial action $\theta$ of a group on a set with an algebraic structure, we construct a reflector of $\theta$ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In…

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…

In 2008, Lehner, Wettig, Guhr and Wei conjectured a power series identity and showed that it implied a determinantal formula for a Bessel-type integral over the unitary supergroup. The integral is the supersymmetric extension of Bessel-type…

According to the classical theorem, every irreducible algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and ${\bf P}^s$…

Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer…

Let $n$ be a positive integer. We introduce a concept, which we call the $n$-filling property, for an action of a group on a separable unital $C^*$-algebra $A$. If $A=C(\Omega)$ is a commutative unital $C^*$-algebra and the action is…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

By jagged partitions we refer to an ordered collection of non-negative integers $(n_1,n_2,..., n_m)$ with $n_m\geq p$ for some positive integer $p$, further subject to some weakly decreasing conditions that prevent them for being genuine…