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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).

Forbidden-minor characterization for the class of graphic element splitting matroids

Kiran Dalvi, Y.M. Borse, M.M. Shikare (2009)

Discussiones Mathematicae Graph Theory

This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solved by proving that there is exactly one minor-minimal matroid that does not have this property.

Frankl’s conjecture for large semimodular and planar semimodular lattices

Gábor Czédli, E. Tamás Schmidt (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A lattice L is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element f ∈ L such that at most half of the elements x of L satisfy f ≤ x . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let m denote the number of nonzero join-irreducible elements of L . It is well-known that L consists of at most 2 m elements....

Graphic Splitting of Cographic Matroids

Naiyer Pirouz (2015)

Discussiones Mathematicae Graph Theory

In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.

Graphs for n-circular matroids

Renata Kawa (2010)

Discussiones Mathematicae Graph Theory

We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].

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