Displaying similar documents to “Dimension stable posets”

A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt (2013)

Discussiones Mathematicae Graph Theory

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.

Dilworth's Decomposition Theorem for Posets

Piotr Rudnicki (2009)

Formalized Mathematics

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The following theorem is due to Dilworth [8]: Let P be a partially ordered set. If the maximal number of elements in an independent subset (anti-chain) of P is k, then P is the union of k chains (cliques).In this article we formalize an elegant proof of the above theorem for finite posets by Perles [13]. The result is then used in proving the case of infinite posets following the original proof of Dilworth [8].A dual of Dilworth's theorem also holds: a poset with maximum clique m is...

On Minimum (Kq, K) Stable Graphs

J.L. Fouquet, H. Thuillier, J.M. Vanherpe, A.P. Wojda (2013)

Discussiones Mathematicae Graph Theory

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A graph G is a (Kq, k) stable graph (q ≥ 3) if it contains a Kq after deleting any subset of k vertices (k ≥ 0). Andrzej ˙ Zak in the paper On (Kq; k)-stable graphs, ( doi:/10.1002/jgt.21705) has proved a conjecture of Dudek, Szyma´nski and Zwonek stating that for sufficiently large k the number of edges of a minimum (Kq, k) stable graph is (2q − 3)(k + 1) and that such a graph is isomorphic to sK2q−2 + tK2q−3 where s and t are integers such that s(q − 1) + t(q − 2) − 1 = k. We have...

Decompositions of saturated models of stable theories

M. C. Laskowski, S. Shelah (2006)

Fundamenta Mathematicae

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We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.

Generalized canonical algebras and standard stable tubes

Andrzej Skowroński (2001)

Colloquium Mathematicae

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We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.