相关论文: Combinatorics of bicubic maps with hard particles
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with…
Constellations and hypermaps generalize combinatorial maps, i.e. embedding of graphs in a surface, in terms of factorization of permutations. In this paper, we extend a result of Jackson and Visentin (1990) stating an enumerative relation…
We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two…
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…
A common problem in graph colouring seeks to decompose the edge set of a given graph into few similar and simple subgraphs, under certain divisibility conditions. In 1987 Wormald conjectured that the edges of every cubic graph on $4n$…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps.…
A planar stuffed map is an embedding of a graph into the 2-sphere $S^{2}$, considered up to orientation-preserving homeomorphisms, such that the complement of the graph is a collection of disjoint topologically connected components that are…
We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We present a novel pairwise IB-representable class of CDCs, CDCs…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of fixed genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the…
A major limitation of exact inference algorithms for probabilistic graphical models is their extensive memory usage, which often puts real-world problems out of their reach. In this paper we show how we can extend inference algorithms,…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
A triangular partition is a partition whose Ferrers diagram can be separated from its complement (as a subset of $\mathbb{N}^2$) by a straight line. Having their origins in combinatorial number theory and computer vision, triangular…
The book embedding of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. A book embedding is matching if the vertices in the same page…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…