Caractérisation, construction et dénombrement des ultramétriques supérieures minimales
Card shuffling and a transformation on Sn.
Cardinalities of D-classes in Bn.
Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties
An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let denote a class of all such properties. In the paper, we consider H-reducible over properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts
We deal with rectangular m×n boards of square cells, using the cut technics of the height function. We investigate combinatorial properties of this function, and in particular we give lower and upper bounds for the number of essentially different cuts. This number turns out to be the cardinality of the height function’s range, in case the height function has maximally many rectangular islands.
Cardinality of Rauzy classes
Rauzy classes form a partition of the set of irreducible permutations. They were introduced as part of a renormalization algorithm for interval exchange transformations. We prove an explicit formula for the cardinality of each Rauzy class. Our proof uses a geometric interpretation of permutations and Rauzy classes in terms of translation surfaces and moduli spaces.
Cartesian subdirect irreducibility in graphs
Catalan monoids, monoids of local endomorphisms, and their presentations.
Catalan numbers modulo .
Catalan numbers, the Hankel transform, and Fibonacci numbers.
Catalan traffic at the beach.
Catalan-Zahlen und Wege in einem ganzzahligen Gitter.
Categorical constructions in graph theory.
Categorical Convolutional Formulas.
Categorification of Hopf algebras of rooted trees
We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring...
Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
Caterpillars
Cayley color graphs of inverse semigroups and groupoids
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap.
Cells and constructible representations in type .