Characterizations of Some Combinatorial Geometries

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We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic ... continued below

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iv, 44 leaves: ill.

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Yoon, Young-jin August 1992.

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  • Yoon, Young-jin

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We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.

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iv, 44 leaves: ill.

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  • August 1992

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  • March 24, 2014, 8:07 p.m.

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  • April 3, 2015, 9:31 a.m.

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Yoon, Young-jin. Characterizations of Some Combinatorial Geometries, dissertation, August 1992; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc277894/: accessed October 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .