Related papers: The Only Complex 4-Net Is the Hesse Configuration

We consider heteroclinic networks between $n \in \mathbb{N}$ nodes where the only connections are those linking each node to its two subsequent neighbouring ones. Using a construction method where all nodes are placed in a single…

We construct a geodesic net in the plane with four boundary (unbalanced) vertices that has 25 balanced vertices and that is irreducible, i.e. it does not contain nontrivial subnets. This net is novel and remarkable for several reasons: (1)…

We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link graphs in the plane that are compatible at the edges and they…

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational CW-complex…

In a minimal binary constraint network, every tuple of a constraint relation can be extended to a solution. The tractability or intractability of computing a solution to such a minimal network was a long standing open question. Dechter…

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic…

We derive necessary and sufficient conditions for order-2 $CP$ ($CP2$) symmetry in $N$-Higgs-doublet potentials for $N>2$. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of…

Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…

In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-connected 3-regular subgraph, whose graph complement is…

Robin Hirsch posed in 1996 the 'Really Big Complexity Problem': classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is…

In this paper we formulate and prove a combinatorial version of the section conjecture for finite groups acting on finite graphs. We apply this result to the study of rational points and show that finite descent is the only obstruction to…

We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure…

Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories, the NS-NS cuplings have been found in a particular scheme which has 445 couplings in 15 different…

Workflow nets are a popular variant of Petri nets that allow for algorithmic formal analysis of business processes. The central decision problems concerning workflow nets deal with soundness, where the initial and final configurations are…

We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil)…

We investigate $k$-nets with $k\geq 4$ embedded in the projective plane $PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$; they are line configurations in $PG(2,\mathbb{K})$ consisting of $k$ pairwise disjoint line-sets, called…

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…

We show that two closed, connected $4$-manifolds with finite fundamental groups are $\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.

The exploration of pathways and alternative pathways that have a specific function is of interest in numerous chemical contexts. A framework for specifying and searching for pathways has previously been developed, but a focus on which of…