Related papers: Enumerating partitions arising in homotopy theory

I present a bijection on integer partitions that leads to recursive expressions, closed formulae and generating functions for the cardinality of certain sets of partitions of a positive integer $n$. The bijection leads also to a product on…

We classify the polynomials with integral coefficients that, when evaluated on a group element of finite order $n$, define a unit in the integral group ring for infinitely many positive integers $n$. We show that this happens if and only if…

One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…

In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…

Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that none of the parts can be written as the sum of smaller…

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also…

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…

In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved

We prove the conjecture by M. Yip stating that counting genus one partitions by the number of their elements and parts yields, up to a shift of indices, the same array of numbers as counting genus one rooted hypermonopoles. Our proof…

Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…

We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in…

A noncommutative and noncocommutative Hopf algebra on finite topologies H_T is introduced and studied (freeness, cofreeness, self-duality...). Generalizing Stanley's definition of P-partitions associated to a special poset, we define the…

Let $d \ge 2, h \ge 1$ be integers. Using a fragmentation technique, we characterise $(h+1)$-tuples $(R_1, \dots, R_h, R)$ of non-empty families of partitions of $\{1, \dots, d\}$ such that it suffices for an order-$d$ tensor to have…

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In…

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…

We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.

It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…

Homomorphisms between relational structures are not only fundamental mathematical objects, but are also of great importance in an applied computational context. Indeed, constraint satisfaction problems (CSPs), a wide class of algorithmic…

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…

We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…