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Dyck paths categories are introduced as a combinatorial model of the category of representations of quivers of Dynkin type An. In particular, it is proved that there is a bijection between some Dyck paths and perfect matchings of some snake…

We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter…

We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…

We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…

We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…

Let $Q$ be a non-degenerated even lattice, let $V_Q$ be the lattice vertex algebra associated to $Q$, and let $V_Q^\eta$ be a quantum lattice vertex algebra. In this paper, we prove the equivalence between the category $V_Q$-modules and the…

The extended weak order on a Coxeter group $W$ is the poset of biclosed sets in its root system. In (Barkley-Speyer 2024), it was shown that when $W=\widetilde{S}_n$ is the affine symmetric group, then the extended weak order is a quotient…

We introduce a method that produces a bijection between the posets ${\rm silt-}{A}$ and ${\rm silt-}{B}$ formed by the isomorphism classes of basic silting complexes over finite-dimensional $k$-algebras $A$ and $B$, by lifting $A$ and $B$…

Using a representation theoretical approach we give an explicit numerical characterization in terms of Kronecker invariants of the subfactor relation between two preinjective (and dually preprojective) Kronecker modules, describing…

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…

We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…

Let $G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy-to-describe bijections $g_{\sigma,\sigma^*}$ between spanning trees of $G$ and $(\sigma,\sigma^*)$-compatible orientations, where…

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…

This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A…

We describe tilting modules of the deformed category O over a semisimple Lie algebra as certain sheaves on a moment graph associated to the corresponding block of category O. We prove that they map to Braden-MacPherson sheaves constructed…

In [J. of Alg. 369: 70-95, 2012], the authors constructed a seven term exact sequence in the cohomology of a group extension G of a normal subgroup N by a quotient group Q with coefficients in a G-module M. However, they were unable to…

Let R be a commutative ring with identity and M be an R-module. In this paper, we introduce and investigate the second submodule intersection graph SSI(M) of M with vertices are nonzero proper submodules of M and two distinct vertices N and…

We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take…

For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an…