Ordonnes escamotables et points fixes

Constantin, Julien; Fournier, Gilles

doi:10.1016/0012-365x(85)90126-8

Cited by 14 publications

(4 citation statements)

References 20 publications

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“…Crowns are well known in the combinatorics of posets, and are associated to their dismantlability (see, for instance, [19,21]). In this paper, we define a notion of dismantlability in an arbitrary schurian algebra.…”

Section: Introductionmentioning

confidence: 99%

Strongly simply connected schurian algebras and multiplicative bases

et al. 2005

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In this paper, we define concepts of crowns and quasi-crowns, valid in an arbitrary schurian algebra, and which generalise the corresponding concepts in an incidence algebra. We show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi-crown. We then prove that the absence of quasi-crowns in a triangular schurian algebra implies the existence of a multiplicative basis.

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Section: Introductionmentioning

confidence: 99%

Strongly simply connected schurian algebras and multiplicative bases

et al. 2005

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“…By Proposition 3.7 in [5], resp. Proposition 4.39 in [18] P and P ∪ {z} have the same homology complex, since (↑ z) \ {z} is dismantlable and thus z is escamotable.…”

Section: Homologymentioning

confidence: 99%

“…[3,5]). Also we can use the above to easily verify that for n ≥ 3, H 0 (B n ) = Z, H n−2 (B n ) = Z and all other homology groups are trivial.…”

Section: Homologymentioning

confidence: 99%

A fixed point theorem with applications to truncated lattices

Rutkowski

Schröder

2005

Algebra univers.

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“…The uniqueness of the fixed-point does not follow directly from our application of Corollary 3.1. We note that the homological methods in [2] have been extended in [3] to apply to comparability-preserving maps on an ordered set.…”

Section: The Equivalence Of the Dismantlability Of G And Clique(g)mentioning

confidence: 99%

Dismantlability Revisited for Ordered Sets and Graphs and the Fixed-Clique Property

Ginsburg¹

1994

Can. math. bull.

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We give a unified treatment of several fixed-point type theorems by using the concept of dismantlability, extended from ordered sets to arbitrary graphs. For a graph G and a vertex x of G we let NG(X) denote the set of neighbours of x in G. We say that x is a subdominant vertex of G if there is a vertex y of G, distinct from x, such that NG(x)∪{x} ⊆ NG(y)∪{y}. If G has n vertices we say that G is dismantlable if the vertices of G can be listed as x1, x2, ..., xi,..., xn such that, for all i = 1,2,..., n— 1, xi is a subdominant vertex of the graph Gi = G — {xj : j < i}

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Ordonnes escamotables et points fixes

Cited by 14 publications

References 20 publications

Strongly simply connected schurian algebras and multiplicative bases

Strongly simply connected schurian algebras and multiplicative bases

A fixed point theorem with applications to truncated lattices

Dismantlability Revisited for Ordered Sets and Graphs and the Fixed-Clique Property

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