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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...

Cancellation rule for internal direct product decompositions of a connected partially ordered set

Ján Jakubík, Mária Csontóová (2000)

Mathematica Bohemica

In this note we deal with two-factor internal direct product decompositions of a connected partially ordered set.

Canonical extensions of Stone and double Stone algebras: the natural way

Miroslav Haviar, Hilary A. Priestley (2006)

Mathematica Slovaca

Canonical ordering theorems, a first attempt

Nešetřil, J., Prömel, H. J., Rödl, V., Voigt, B. (1982)

Proceedings of the 10th Winter School on Abstract Analysis

Canonical partition theorems for finite distributive lattices

Prömel, H. J., Voigt, B. (1982)

Proceedings of the 10th Winter School on Abstract Analysis

Cantor extension of a half lattice ordered group

Štefan Černák (1998)

Mathematica Slovaca

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 extension of a mixed product of directed groups

Štefan Černák (1976)

Mathematica Slovaca

Cantor extension of an Abelian cyclically ordered group

Štefan Černák (1989)

Mathematica Slovaca

Cantor-Bernstein theorem for lattice ordered groups

Ján Jakubík (1972)

Czechoslovak Mathematical Journal

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.

Cantor-Bernstein theorem for $M V$ -algebras

Ján Jakubík (1999)

Czechoslovak Mathematical Journal

Caractérisation du type d'ordre des barrières de Nash-Williams

Marc Assous (1974)

Publications du Département de mathématiques (Lyon)

Caractérisations axiomatiques de la distance de la différence symétrique entre des relations binaires

Jean-Pierre Barthelemy (1979)

Mathématiques et Sciences Humaines

Caractérisations métriques des ensembles ordonnés semi-modulaires

B. Monjardet (1977)

Mathématiques et Sciences Humaines

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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