One view of the metamorphic subduction system supposes that coupled deformation and prograde/metasomatic reaction between the chemically enriched slab and the depleted mantle wedge promotes the formation of complexly hybridized lithologies along the slab/mantle interface. This type of model is based upon direct observations of the structure and petrology of high-P/T metamorphic complexes (e.g.,...

We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...

For G a finite abelian group, we study the properties of general equivalence relations on Gn = Gn Sn , the wreath product of G with the symmetric group Sn , also known as the G-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of kGn as well as graded connected Hopf subalgebras of ⊕ n≥o kGn . In particular we construct a G-colou...

In this short note, we study pairwise edge-disjoint rainbow spanning trees in properly edge-coloured complete graphs, where a graph is rainbow if its edges have distinct colours. Brualdi and Hollingsworth conjectured that every Kn properly edge-coloured by n−1 colours has n/2 edge-disjoint rainbow spanning trees. Kaneko, Kano and Suzuki later suggested this should hold for every properly edge-c...

A Helly-type theorem for diameter provides a bound on the of intersection finite family convex sets in $\mathbb{R}^d$ given some information all sufficiently small subfamilies. We prove fractional and colorful versions long-standing conjecture by Bárány, Katchalski, Pach. also show that Minkowski norm admits an exact if only its unit ball is polytope version those do. Finally, we theorems prope...

In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, for n sufficiently large, we determine the minimum number of monochromatic triangles in a 3-coloured copy of K...

Abstract. We introduce the concept of a morphism between coloured nets. Our definition generalizes Petris definition for ordinary nets. A morphism of coloured nets maps the topological space of the underlying undirected net as well as the kernel and cokernel of the incidence map. The kernel are flows along the transitionbordered fibres of the morphism, the cokernel are classes of markings of th...

We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the following conjecture by B. Bollobás and P. Erdős (1976) : if G is an edge-coloured complete graph on n vertices in which the maximum monochromatic degree of every vertex is less than bn/2c, then G contains a PC Hamiltonian cyc...

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach. Lett. Math. Phys. 53 (2000) 29-4...