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An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra $\mathfrak{q}$ that are equivariant with respect to the action of a finite group…
In this paper, we show that computing canonical labelings of graphs of bounded rank-width is in $\textsf{TC}^{2}$. Our approach builds on the framework of K\"obler & Verbitsky (CSR 2008), who established the analogous result for graphs of…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…
The Weisfeiler-Leman (WL) dimension is an established measure for the inherent descriptive complexity of graphs and relational structures. It corresponds to the number of variables that are needed and sufficient to define the object of…
Let $X$ be an arbitrary poset and $K$ an arbitrary field. We describe linear unital invertibility preservers of the finitary incidence algebra $FI(X,K)$ in terms of certain maps of the power set algebra $\mathcal{P}(X)$ and linear maps…
It is well known that two finite sequences of vectors in inner product spaces are unitarily equivalent if and only if their respective inner products (Gram matrices) are equal. Here we present a corresponding result for the projective…
We give an isomorphism test for graphs of Euler genus $g$ running in time $2^{O(g^4 \log g)}n^{O(1)}$. Our algorithm provides the first explicit upper bound on the dependence on $g$ for an fpt isomorphism test parameterized by the Euler…
This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…
We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…
This paper is concerned with the algebraic K-theory of locally convex algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that the obstruction for the comparison map between algebraic and…
Let $v$ be a vertex of a graph $G$. By the local complementation of $G$ at $v$ we mean to complement the subgraph induced by the neighbors of $v$. This operator can be generalized as follows. Assume that, each edge of $G$ has a label in the…
The Gruenberg-Kegel graph (or the prime graph) $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an…
Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
We study the expressive power of first-order logic with counting quantifiers, especially the $k$-variable and quantifier-rank-$q$ fragment $\mathsf{C}^k_q$, using homomorphism indistinguishability. Recently, Dawar, Jakl, and Reggio (2021)…
It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…
K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the…
For a map $\varphi : \varGamma \rightarrow \varGamma^{\prime}$ between metric graphs and an isometric action on $\varGamma$ by finite group $K$, $\varphi$ is a $K$-Galois covering on $\varGamma^{\prime}$ if $\varphi$ is a morphism, the…
Constraint satisfaction (CSP) and structure isomorphism (SI) are among the most well-studied computational problems in Computer Science. While neither problem is thought to be in $\texttt{PTIME},$ much work is done on $\texttt{PTIME}$…