The rank of a cograph.
Royle, Gordon F. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Royle, Gordon F. (2003)
The Electronic Journal of Combinatorics [electronic only]
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John T. Baldwin, Kitty Holland (2001)
Fundamenta Mathematicae
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This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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A. Lachlan (1974)
Fundamenta Mathematicae
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Robert J. Archbold, Eberhard Kaniuth (2006)
Studia Mathematica
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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
A. Lachlan (1980)
Fundamenta Mathematicae
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Cioabă, Sebastian M., Tait, Michael (2011)
The Electronic Journal of Combinatorics [electronic only]
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Dobrynin, V.Y. (1997)
The Electronic Journal of Combinatorics [electronic only]
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Irina Gelbukh (2015)
Czechoslovak Mathematical Journal
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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...
Cordovil, Raúl, Guedes de Oliveira, A., Moreira, M. Leonor (1988)
Portugaliae mathematica
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