A coloring c of the vertices of a graph G is nonrepetitive if there exists no path v1v2 . . . v2l for which c(vi) = c(vl+i) for all 1 ≤ i ≤ l. Given graphs G and H with |V (H)| = k, the lexicographic product G[H ] is the graph obtained by substituting every vertex of G by a copy of H , and every edge of G by a copy of Kk,k. We prove that for a sufficiently long path P , a nonrepetitive coloring...

To deal with the curse of dimensionality in high dimensional nonparamet-ric problems, we consider using tensor product space ANOVA models, which extend the popular additive models and are able to capture interactions of any order. The multivariate function is given an ANOVA decomposition, i.e, it is expressed as a constant plus the sum of functions of one variable (main eeects), plus the sum of...

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1) × G(V2) be a pair of classical groups diagonally embedded in G(V1 ⊕ V2). Suppose that dimV1 < dimV2. Let π be a discrete series representation of G(V1 ⊕ V2). We prove that the functor π⊗G(V1) maps unitary representations of G(V1) to unitary representat...

Consider a simple connected graph $$G = (V,E)$$ of order p and size q. For bijection $$f : E \to \{1,2,\ldots,q\}$$ , let $$f^+(u) \sum_{e\in E(u)} f(e)$$ where $$E(u)$$ is the set edges incident to u. We say f local antimagic labeling G if for any two adjacent vertices u v, we have \ne f^+(v)$$ . The minimum number distinct values $$f^+$$ taken over all denoted by $$\chi_{la}(G)$$ Let $$G[H]$$...