Related papers: Free crossed resolutions from simplicial resolutio…
The aim of this paper is to give a simple construction of the free skew-brace over a set $X$.
We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at…
For a free partial action of a group in a set we realize the associated partial skew group ring as an algebra of functions with finite support over an equivalence relation and we use this result to characterize the ideals in the partial…
Given a monomial ideal $I$ with minimal free resolution $\mathcal{F}$ supported in characteristic $p>0$ on a CW-complex $X$ with regular $2$-skeleton, we construct a CW-complex $Y$ that also supports~$\mathcal{F}$ and such that the face…
Given a finite CAT(0) cubical complex, we define a flag simplicial complex associated to it, called the crossing complex. We show that the crossing complex holds much of the combinatorial information of the original cubical complex: for…
We propose some conditions on a poset that produce a small chain complex for its homology. This allows to compare simplicial complexes and Quillen's complexes under the same prism. It turns out they differ in the existence or not of free…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
The purpose of this paper is to give new examples of families of free singularities. We first show that a generic equidimensional subspace arrangement is free. Furthermore, we show that a product of two reduced Cohen-Macaulay subspaces is…
We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.
In [Discrete differential calculus on simplicial complexes and constrained homology, Chin. Ann. Math. Ser. B 44(4), 615-640, 2023], the constrained (co)homology for simplicial complexes and independence hypergraphs is constructed via…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
A combinatorial formula is derived which expresses free cumulants in terms of classical comulants. As a corollary, we give a combinatorial interpretation of free cumulants of classical distributions, notably Gaussian and Poisson…
We give a topological interpretation of the free metabelian group, following the plan described in [Ver1,Ver2]. This interpretation is based on considering the Caley graph of a finitely generated group G as one-dimensional complex; its…
We study the free complexification operation for compact quantum groups, $G\to G^c$. We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free…
We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse complex. Even…
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
What are the subcomplexes of a free resolution? This question is simple to state, but the naive approach leads to a computational quagmire that is infeasible even in small cases. In this paper, we invoke the Bernstein--Gelfand--Gelfand…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…
In this paper, we consider free transposed Poisson algebra and free F-manifold algebra with an additional metabelian identity. We construct a linear basis for both free metabelian transposed Poisson algebra and free metabelian F-manifold…
This note is to show the effectiveness of the notion of pseudoalgebra in the theory of conformal algebras. We adduce very simple construction of free associative conformal algebra and find its linear basis. There is no any new result but we…