State space properties of finite logics
Stationary map coloring
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the Poisson process. As part of the proof we show that the 6-core of the corresponding Delaunay triangulation is empty. Generalizations, extensions and some open questions are discussed.
Stationary random graphs on with prescribed iid degrees and finite mean connections.
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Statistics on Dyck paths.
Statistics on the multi-colored permutation groups.
Statuses and branch-weights of weighted trees
In this paper we show that in a tree with vertex weights the vertices with the second smallest status and those with the second smallest branch-weight are the same.
Statuses and double branch weights of quadrangular outerplanar graphs
In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs
Steiner distance in graphs
Steiner Minimal Trees for Regular Polygons.
Steiner Minimal Trees on Sets of Four Points.
Steiner Systems which Admit Block Transitive Automorphism Groups of Small Rank.
Steiner triple systems and existentially closed graphs.
Steiner triple systems intersecting in pairwise disjoint blocks.
Steinhaus chessboard theorem
Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics
Stirling pairs
Stopping Markov processes and first path on graphs
Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....
Straight line representations of planar graphs.
Straight-line drawings of binary trees with linear area and arbitrary aspect ratio.