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Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

For a finite Coxeter group W and a Coxeter element c of W ; the c -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W . Its maximal cones are naturally indexed by the c -sortable elements of W . The main result of this paper is that the known bijection cl c between c -sortable elements and c -clusters induces a combinatorial isomorphism of fans. In particular, the c -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for W . The rays...

Cantor extension of a half lineary cyclically ordered group

Štefan Černák (2001)

Discussiones Mathematicae - General Algebra and Applications

Convergent and fundamental sequences are studied in a half linearly cyclically ordered group G with the abelian increasing part. The main result is the construction of the Cantor extension of G.

Cantor-Bernstein theorem for lattices

Ján Jakubík (2002)

Mathematica Bohemica

This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.

Cardinal and ordinal arithmetics of n -ary relational systems and n -ary ordered sets

Jiří Karásek (1998)

Mathematica Bohemica

The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for n -ary relational systems. n -ary ordered sets are defined as special n -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of n = 2 or 3. The class of n -ary ordered sets is then closed under the cardinal and ordinal operations.

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