Volumen 17 (2013) No. 1

Partial monoids and Dold-Thom functors

Jacob Mostovoy

Resumen:

Dold-Thom functors generalize infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the machinery of $\Gamma$-spaces produces the corresponding linear Dold-Thom functor. In this note we construct such functors directly from spectra by exhibiting a partial monoid corresponding to a spectrum.

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Álgebra $C^∗$ generada por operadores de Toeplitz con símbolos discontinuos en el espacio de Bergman armónico

Maribel Loaiza and Carmen Lozano

Resumen:

Sea $l$ una curva simple suave en el disco unitario complejo $\mathbb{D}$. En este trabajo estudiamos el álgebra de Calkin del álgebra $C^∗$ generada por operadores de Toeplitz que actuán en el espacio de Bergman armónico de $\mathbb{D}$, cuyos símbolos son funciones continuas en $\overline{\mathbb{D}} \setminus l$. El resultado principal e inesperado es que el espectro de un operador de Toeplitz cuyo símbolo es una función constante a trozos depende del ángulo de discontinuidad.

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Ideals, varieties, stability, colorings and combinatorial designs

Javier Muñoz, Feliú Sagols, and Charles J. Colbourn

Resumen:

A combinatorial design is equivalent to a stable set in a suitably chosen Johnson graph, whose vertices correspond to all $k$-sets that could be blocks of the design. In order to find maximum stable sets of a graph $G$, two ideals are associated with $G$, one constructed from the Motzkin-Strauss formula and one reported by Lova ́sz in connection with the stability polytope. These ideals are shown to coincide and form the stability ideal of $G$. Graph stability ideals belong to a class of $0-1$ ideals. These ideals are shown to be radical, and therefore have a strong structure.

Stability ideals of Johnson graphs provide an algebraic char- acterization that can be used to generate Steiner triple systems. Two different ideals for the generation of Steiner triple systems, and a third for Kirkman triple systems, are developed. The last of these combines stability and colorings.

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