Related papers: The Gamma question for many-one degrees

For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…

The $1/2$-conjecture on the domination game asserts that if $G$ is a traceable graph, then the game domination number $\gamma_g(G)$ of $G$ is at most $\left\lceil \frac{n(G)}{2} \right\rceil$. A traceable graph is a $1/2$-graph if…

What minimum degree of a graph $G$ on $n$ vertices guarantees that the union of $G$ and a random $2$-factor (or permutation) is with high probability Hamiltonian? Gir\~ao and Espuny D{\'\i}az showed that the answer lies in the interval…

We develop an improved bound for the chromatic number of graphs of maximum degree $\Delta$ under the assumption that the number of edges spanning any neighbourhood is at most $(1-\sigma)\binom{\Delta}{2}$ for some fixed $0<\sigma<1$. The…

A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \Gamma. We study how hard it is to evaluate this number approximately. There is an…

We construct an increasing $\omega$-sequence $(a_n)$ of Turing degrees which forms an initial segment of the Turing degrees, and such that each~$a_{n+1}$ is diagonally noncomputable relative to $a_n$. It follows that the~$\mathsf{DNR}$…

We discuss sufficiently fast-growing sequences of Turing degrees. The key result is that, assuming sufficient determinacy, if $\phi$ is a formula with one free variable, and S and T are sufficiently fast-growing sequences of Turing degrees…

Let K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,\Gamma)$ for the number of solutions…

A subset $D \subseteq V $of a graph $G = (V, E)$ is a $(1, j)$-set if every vertex $v \in V \setminus D$ is adjacent to at least $1$ but not more than $j$ vertices in D. The cardinality of a minimum $(1, j)$-set of $G$, denoted as…

The normal covering number $\gamma(G)$ of a finite group $G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for $\gamma(S_n)$ and $\gamma(A_n)$ depending on the arithmetic structure of…

Given a graph $\Gamma = (V, E)$ on $n$ vertices and $m$ edges, we define the Erd\H{o}s-R\'{e}nyi graph process with host $\Gamma$ as follows. A permutation $e_1,\dots,e_m$ of $E$ is chosen uniformly at random, and for $t\leq m$ we let…

We consider a connected graph $\Gamma$ as a coarse space and prove that $\Gamma$ admits a 2-selector if and only if $\Gamma$ is either bounded or coarsely equivalent to $\mathbb{N}$ or $\mathbb{Z}$. We apply this result to geodesic metric…

Fix $c\in (0,1)$ and let $\Gamma$ be a $\lfloor c n\rfloor$-regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency matrix $M$ of $\Gamma$ is invertible with high…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

The classification, by topological conjugacy, of invertible holomorphic germs $f:(\mathbb{C}^n,0)\to (\mathbb{C}^n,0)$, with $\lambda_1,...,\lambda_n$ eigenvalues of $df_0$, and $|\lambda_i|\neq 1$ for $i=2,...,n$ while $\lambda_1$ is a…

Aims. An attempt to classify gamma-ray bursts (GRBs) with a low level of supervision using the state-of-the-start approaches stemming from graph theory was undertaken. Methods. Graph-based classification methods, relying on different…

We prove that for every graph $G$ on $n$ vertices and with minimum degree five, the domination number $\gamma(G)$ cannot exceed $n/3$. The proof combines an algorithmic approach and the discharging method. Using the same technique, we…

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo…

Let $\Gamma$ be a discrete group. We show that if $\Gamma$ is nonamenable, then the algebraic tensor products $C^*_r(\Gamma)\otimes C^*_r(\Gamma)$ and $C^*(\Gamma)\otimes C^*_r(\Gamma)$ do not admit unique $C^*$-norms. Moreover, when…

Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem that has been extensively studied in recent years. We study a hypergraph version of the problem. Let $G^r(n,p)$ denote the…