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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...

Cofinal types of topological directed orders

SŁawomir Solecki, Stevo Todorcevic (2004)

Annales de l’institut Fourier

We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.

Coloring digraphs by iterated antichains

Svatopluk Poljak (1991)

Commentationes Mathematicae Universitatis Carolinae

We show that the minimum chromatic number of a product of two n -chromatic graphs is either bounded by 9, or tends to infinity. The result is obtained by the study of coloring iterated adjoints of a digraph by iterated antichains of a poset.

Combinatoria e Topologia. Alcune considerazioni generali

Andrea Brini (2003)

Bollettino dell'Unione Matematica Italiana

Si descrive un metodo generale mediante il quale associare in modo naturale spazi topologici ad insiemi parzialmente ordinati e funzioni continue afunzioni monotone tra di essi; questa associazione è chiaramente la chiave di volta per fondare l’utilizzo di metodi topologici nella teoria combinatoria degli insiemi parzialmente ordinati. Si discutono quindi alcuni criteri di contraibilità e si presenta una breve introduzione alla teoria dei «poset Cohen-Macaulay». Il lavoro si conclude con una sezione...

Combinatorial construction of toric residues.

Amit Khetan, Ivan Soprounov (2005)

Annales de l’institut Fourier

In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n = 2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier...

Commutative directoids with sectionally antitone bijections

Ivan Chajda, Miroslav Kolařík, Sándor Radeleczki (2008)

Discussiones Mathematicae - General Algebra and Applications

We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.

Counting biorders.

Christophe, Julie, Doignon, Jean-Paul, Fiorini, Samuel (2003)

Journal of Integer Sequences [electronic only]

Coxeter-like complexes.

Babson, Eric, Reiner, Victor (2004)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Cycle-free cuts of mutual rank probability relations

Karel De Loof, Bernard De Baets, Hans De Meyer (2014)

Kybernetika

It is well known that the linear extension majority (LEM) relation of a poset of size n ≥ 9 can contain cycles. In this paper we are interested in obtaining minimum cutting levels α m such that the crisp relation obtained from the mutual rank probability relation by setting to 0 its elements smaller than or equal to α m , and to 1 its other elements, is free from cycles of length m . In a first part, theoretical upper bounds for α m are derived using known transitivity properties of the mutual rank probability...

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