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Embedding properties of endomorphism semigroups

João Araújo, Friedrich Wehrung (2009)

Fundamenta Mathematicae

Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff c a r d Γ 2 c a r d Ω . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...

Étude des tresses de Gutmann en algèbre à P valeurs

Y. Kergall (1974)

Mathématiques et Sciences Humaines

La notion de tresse de Gutmann a été introduite ([4]) pour généraliser la notion de chaîne de Gutmann qui restait souvent assez loin du protocole observé. Les tresses de Gutmann ont été étudiées ([3], [4], [6]) en considérant que les réponses au questionnaire étaient dichotomiques. Nous supposons ici que les réponses aux questions appartiennent à un ensemble fini totalement ordonné quelconque.

Exact Expectation and Variance of Minimal Basis of Random Matroids

Wojciech Kordecki, Anna Lyczkowska-Hanćkowiak (2013)

Discussiones Mathematicae Graph Theory

We formulate and prove a formula to compute the expected value of the minimal random basis of an arbitrary finite matroid whose elements are assigned weights which are independent and uniformly distributed on the interval [0, 1]. This method yields an exact formula in terms of the Tutte polynomial. We give a simple formula to find the minimal random basis of the projective geometry PG(r − 1, q).

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