Related papers: Flag Algebras: A First Glance
We give a combinatorial rule for computing intersection numbers on a flag manifold which come from products of Schubert classes pulled back from Grassmannian projections. This rule generalizes the known rule for Grassmannians.
Patchworking is a construction of a one-parameter family of real algebraic hypersurfaces. For sufficiently small positive values of the parameter, the hypersurfaces can be obtained by gluing of given hypersurfaces topologically. The author…
Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., complex systems in physics, computer science, social sciences,…
In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a…
In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type $ADE$ carries a structure of $P/Q$-graded vertex operator algebra. There exists a filtration on this direct sum studied by…
Extremal Graph Theory aims to determine bounds for graph invariants as well as the graphs attaining those bounds. We are currently developping PHOEG, an ecosystem of tools designed to help researchers in Extremal Graph Theory. It uses a big…
When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is…
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
For a $k$-uniform hypergraph $F$ let $\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\textrm{ex}(n,F)$ is a classical and central problem…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group $\mathbb{G}$ the class of operators which acts on $L^{2}(\mathbb{G})$ by convolution with a flag kernel is closed under…
We obtain the Phragm\`en-Lindel\"of principle on combinatorial infinite weighted graphs for the Cauchy problem associated to a certain class of parabolic equations with a variable density. We show that the hypothesis made on the density is…
We study Kirillov algebras attached to minuscule highest weight representations of semisimple Lie algebras. They can be viewed as equivariant cohomology algebras of partial flag varieties. Real structures on the varieties then induce…