Related papers: Actions and identities on set partitions

We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and the character for the action of the symmetric groups on…

We define the decomposition property for partial actions of discrete groups on $C^*$-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions…

Let $X$ be an algebraic variety over $\mathbb{C}$ and $G$ be an algebraic group acting on $X$ whose action is closed. J. Poineau defined a compactification $X^\urcorner$ of $X(\mathbb{C})$ by using hybrid Berkovich spaces. We will focus on…

We give examples of principal algebraic actions of the noncommutative free group $F$ of rank two, as well as other groups, by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism to a…

This paper studies partitions in the space of antimonotonic boolean functions on sets of n elements. The antimonotonic functions are the antichains of the partially ordered set of subsets. We analyse and characterise a natural partial…

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

We generalize Gruber--Sisto's construction of the coned--off graph of a small cancellation group to build a partially ordered set $\mathcal{TC}$ of cobounded actions of a given small cancellation group whose smallest element is the action…

Let S and T be sets of positive integers and let a be a fixed positive integer. An a-shifted partition identity has the form p(S,n)=p(T,n-a), for all n greater or equal to a. Here p(S,n) is the number partitions of n whose parts are…

Partitions of [n]={1,2,...,n} into sets of lists are counted by sequence number A000262 in the On-Line Encyclopedia of Integer Sequences. They are somewhat less numerous than partitions of [n] into lists of sets, A000670. Here we observe…

A $(k,\ell )$ partial partition of an $n$-element set is a collection of $\ell $ pairwise disjoint $k$-element subsets. It is proved that, if $n$ is large enough, one can find $\left\lfloor {n\choose k}/{\ell}\right\rfloor$ such partial…

Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are…

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic…

Let $A$ be a unital associative PI-algebra over a field of characteristic zero. We study which partitions $\lambda$ appear with nonzero multiplicities in the cocharacter sequence of $A$ for several classes of algebras $A$. Berele defines…

Let $\overline{\mathrm{spt}}k(n)$ denote the number of overpartitions of $n$ where the smallest non-overlined part, say $s(\pi)$, appears $k$ times and every overlined part is bigger than $s(\pi)$. Let $\overline{\mathrm{spt}}k_o(n)$ denote…

We describe a connection between the subjects of cluster algebras, polynomial identity algebras and discriminants. For this, we define the notion of root of unity quantum cluster algebras and prove that they are polynomial identity…

In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of…

In the quantum theory, using the notion of partial supersymmetry, in which some, but not all, operators have superpartners we derive the Euler theorem in partition theory. The paraferminic partition function gives another identity in…

In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.

The superspace ring $\Omega_n$ is a rank $n$ polynomial ring tensor a rank $n$ exterior algebra. Using an extension of the Vandermonde determinant to $\Omega_n$, the authors previously defined a family of doubly graded quotients…