A 2-coloring of can have monochromatic Schur triples, but not less.
-analogue of some binomial coefficient identities of Y. Sun.
A backward selection procedure for approximating a discrete probability distribution by decomposable models
Decomposable (probabilistic) models are log-linear models generated by acyclic hypergraphs, and a number of nice properties enjoyed by them are known. In many applications the following selection problem naturally arises: given a probability distribution over a finite set of discrete variables and a positive integer , find a decomposable model with tree-width that best fits . If is the generating hypergraph of a decomposable model and is the estimate of under the model, we can measure...
A bi-average tree solution for probabilistic communication situations with fuzzy coalition
A probabilistic communication structure considers the setting with communication restrictions in which each pair of players has a probability to communicate directly. In this paper, we consider a more general framework, called a probabilistic communication structure with fuzzy coalition, that allows any player to have a participation degree to cooperate within a coalition. A maximal product spanning tree, indicating a way of the greatest possibility to communicate among the players, is introduced...
A bijection between 3-Motzkin paths and Schröder paths with no peak at odd.
A bijection between atomic partitions and unsplitable partitions.
A bijection between classes of fully packed loops and plane partitions.
A bijection between planar constellations and some colored Lagrangian trees.
A bijection on Dyck paths and its cycle structure.
A bijective proof of a major index theorem of Garsia and Gessel.
A bijective proof of Borchardt's identity.
A bijective proof of Garsia's -Lagrange inversion theorem.
A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin.
A binomial coefficient identity associated to a conjecture of Beukers.
A binomial coefficient identity associated with Beukers' conjecture on Apéry numbers.
A binomial representation of the 3x + 1 problem
A bisection method for the traveling salesman problem
A bound for size Ramsey numbers of multipartite graphs.
A bound for the rank-one transient of inhomogeneous matrix products in special case
We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.
A bound for the Steiner tree problem in graphs