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Construction of Mendelsohn designs by using quasigroups of ( 2 , q ) -varieties

Lidija Goračinova-Ilieva, Smile Markovski (2016)

Commentationes Mathematicae Universitatis Carolinae

Let q be a positive integer. An algebra is said to have the property ( 2 , q ) if all of its subalgebras generated by two distinct elements have exactly q elements. A variety 𝒱 of algebras is a variety with the property ( 2 , q ) if every member of 𝒱 has the property ( 2 , q ) . Such varieties exist only in the case of q prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property ( 2 , q ) , 2 < q , blocks of Steiner system of type ( 2 , q ) are obtained. The stated correspondence between Steiner...

Coxeter polynomials of Salem trees

Charalampos A. Evripidou (2015)

Colloquium Mathematicae

We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities m , . . . , m k for the Coxeter polynomials of the trees , . . . , k respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least m i n m - m , . . . , m - m k where m = m + + m k .

Coxeter-like complexes.

Babson, Eric, Reiner, Victor (2004)

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

Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

Peng Shan (2011)

Annales scientifiques de l'École Normale Supérieure

We define the i -restriction and i -induction functors on the category 𝒪 of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.

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