Related papers: Rational Mixed Tate Motivic Graphs
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
We construct indecomposable cycles in the motivic cohomology group $H^3_{{\mathcal M}}(A,{\mathbb Q}(2))$ where $A$ is an Abelian surface over a number field or the function field of a base. When $A$ is the self product of the universal…
In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…
We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by…
We formulate a combinatorial version of the Intersection Hodge Conjecture for projective toric varieties. The conjecture asserts that the subspace of rational Hodge classes in the intersection cohomology $IH^*(X_\Sigma)$ is generated by the…
We consider families of coded systems that contain the Dyck shifts and that are closed under topological conjugacy. We introduce a notion of hyposynchronization of subshifts. We introduce a notion of restricted complexity of…
This is a considerably expanded version of the "pure" part of our 2002 preprint. We define a category of pure birational motives over a field, depending on the choice of an adequate equivalence relation on algebraic cycles. It is obtained…
Large knowledge graphs capture information of a large number of entities and their relations. Among the many relations they capture, class subsumption assertions are usually present and expressed using the \texttt{rdfs:subClassOf}…
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labeled graphs that were used to construct canonical bases in…
The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…
We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear…
In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of…
A biased graph consists of a graph $G$ together with a collection of distinguished cycles of $G$, called balanced cycles, with the property that no theta subgraph contains exactly two balanced cycles. Perhaps the most natural biased graphs…
The Feynman amplitude associated to a graph is a period of a certain motive. The sum of these motive classes over all connected graphs with no multiple edges or tadpoles and n vertices is defined in the Grothendieck ring of varieties. This…
Crossword puzzles lend themselves to mathematical inquiry. Several authors have already described the arrangement of crossword grids and associated combinatorics of answer numbers. In this paper, we present a new graph-theoretic…
The goal of this article is to try understand where Hodge cycles on a singular complex projective variety X come from. As a first step we consider Hodge cycles on the maximal pure quotient $H^{2p}(X)/W_{2p-1}$, and introduce a class of…
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…