Displaying similar documents to “Valuations of lines”

Dimensional compactness in biequivalence vector spaces

J. Náter, P. Pulmann, Pavol Zlatoš (1992)

Commentationes Mathematicae Universitatis Carolinae

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The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a π -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set s and classes of set...

Monotonic valuations of π σ -triads and evaluations of ideals

Josef Mlček (1993)

Commentationes Mathematicae Universitatis Carolinae

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We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type π σ is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal J of the type π on a set A , a monotone and subadditive set-mapping h on P ( A ) with values in non-negative rational numbers such that J = h - 1 ' ' { r ∈ Q ; r ≥ 0 & r ≐ 0 } . Some analogical results are proved for ideals of the...

Degree sequences of graphs containing a cycle with prescribed length

Jian Hua Yin (2009)

Czechoslovak Mathematical Journal

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Let r ≥ 3 , n ≥ r and π = ( d 1 , d 2 , ... , d n ) be a non-increasing sequence of nonnegative integers. If π has a realization G with vertex set V ( G ) = { v 1 , v 2 , ... , v n } such that d G ( v i ) = d i for i = 1 , 2 , ... , n and v 1 v 2 ⋯ v r v 1 is a cycle of length r in G , then π is said to be potentially C r ' ' -graphic. In this paper, we give a characterization for π to be potentially C r ' ' -graphic.