相关论文: Characterizing Rothe Diagrams

Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…

The rotor-router model on a graph describes a discrete-time walk accompanied by the deterministic evolution of configurations of rotors randomly placed on vertices of the graph. We prove the following property: if at some moment of time,…

We characterise those permutation classes whose simple permutations are monotone griddable. This characterisation is obtained by identifying a set of nine substructures, at least one of which must occur in any simple permutation containing…

A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is…

A rotor-router walk is a deterministic version of a random walk, in which the walker is routed to each of the neighbouring vertices in some fixed cyclic order. We consider here directed covers of graphs (called also periodic trees) and we…

We give a combinatorial description for when the Specht module of an arbitrary diagram admits a (complete) branching rule. This description, given in terms of the maximal rectangles of the diagram, generalizes all previously known branching…

Let $\rho(G)$ denote the number of convex cycles of a simple graph G of order n, size m, and girth 3 <= g <=n. It is proved that $\rho(G) \leq \frac{n}{g}(m-n+1)$ and that equality holds if and only if G is an even cycle or a Moore graph.…

Firstly, for a general graph, we find a recursion formula on the number of Hamiltonian cycles and one on cycles. By this result, we give some new polynomial invariants. Secondly, we give a condition to tell whether a polynomial defined by…

We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices $n$, as first established in recent work with…

A drawing of a graph is 1-planar if each edge participates in at most one crossing and adjacent edges do not cross. Up to symmetry, each crossing in a 1-planar drawing belongs to one out of six possible crossing types, where a type…

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota-Baxter algebra, called the Rota-Baxter characteristic. We introduce an invariant, called the ascent set, of a…

We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously.…

We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…

A monotone drawing of a graph G is a straight-line drawing of G such that every pair of vertices is connected by a path that is monotone with respect to some direction. Trees, as a special class of graphs, have been the focus of several…

The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations…

Frequently, knots are enumerated by their crossing number. However, the number of knots with crossing number $c$ grows exponentially with $c$, and to date computer-assisted proofs can only classify diagrams up to around twenty crossings.…

We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every…