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The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...

Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...