The KP equation is a nonlinear dispersive wave which provides an excellent model for resonant interactions of shallow-water waves. It well known that regular soliton solutions the may be constructed from points in totally nonnegative Grassmannian Gr(N,M)?0. Kodama and Williams studied asymptotic patterns (tropical limit) solitons, called graphs, showed they correspond to Postnikov's Le-diagrams...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...

The commuting graph C(G,X) , where G is a group and X a subset of G, has X as its vertex set with two distinct elements of X joined by an edge when they commute in G. Here the diameter and disc structure of C(G,X) is investigated when G is the symmetric group and X a conjugacy class of G.

Let G be a non-abelian finite group. In this paper, we prove that Γ(G) is K4-free, if and only if G ∼= A× P , where A is an abelian group, P is a 2-group and G/Z(G) ∼= Z2 × Z2. Also, we show that Γ(G) is K1,3-free if and only if G ∼= S3, D8 or Q8.

Received by the editors on July 11, 2012. Accepted for publication on May 26, 2013. Handling Editor: Michael Tsatsomeros. Department of Mathematics, University of Ljubljana, Slovenia ([email protected], [email protected]). Supported by Research Programs P1-0222 and L1-069 of the Slovenian Research Agency. Department of Computer and Information Science, University of Ljubl...

Let S be a finite non-commutative semigroup. The commuting graph of S, denoted G(S), is the graph whose vertices are the non-central elements of S and whose edges are the sets {a, b} of vertices such that a 6= b and ab = ba. Denote by T (X) the semigroup of full transformations on a finite set X. Let J be any ideal of T (X) such that J is different from the ideal of constant transformations on ...

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Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...