منابع مشابه
Split semiorders
A poset P = (X, 4 ) is a split semiorder if there are maps a , f : X --* • with a(x)<~f(x)<~a(x) + 1 for every x E X such that x -< y if and only if f ( x ) < a ( y ) and a(x) + 1 < f ( y ) . A split interval order is defined similarly with a(x)+ 1 replaced by b(x), a(x)<~ f(x)<~ b(x), such that x -< y if and only if f ( x ) < a ( y ) and b(x) < f ( y ) . We investigate these generalizations of...
متن کاملDimensions of Split Semiorders
A poset P = (X,P ) is a split semiorder when there exists a function I that assigns to each x ∈ X a closed interval I (x) = [ax, ax + 1] of the real line R and a set F = {fx : x ∈ X} of real numbers, with ax ≤ fx ≤ ax +1, such that x < y in P if and only if fx < ay and ax +1 < fy in R. Every semiorder is a split semiorder, and there are split semiorders which are not interval orders. It is well...
متن کاملFractional weak discrepancy and split semiorders
The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [5] as the minimum nonnegative k for which there exists a function f : V → R satisfying (i) if a ≺ b then f(a)+1 ≤ f(b) and (ii) if a ‖ b then |f(a) − f(b)| ≤ k. In this paper we generalize results in [6, 7] on the range of wdF for semiorders to the larger class of split semiorders. In particular, we prove that for ...
متن کاملSemiorders with separability properties
We analyze different separability conditions that characterize the numerical representability of semiorders through a real-valued function and a strictly positive threshold. Any necessary and sufficient condition for the numerical representability of an interval order by means of two real-valued functions is proved to also characterize the Scott–Suppes representability of semiorders provided th...
متن کاملSemiorders and Riordan Numbers
In this paper, we define a class of semiorders (or unit interval orders) that arose in the context of polyhedral combinatorics. In the first section of the paper, we will present a pure counting argument equating the number of these interesting (connected and irredundant) semiorders on n + 1 elements with the nth Riordan number. In the second section, we will make explicit the relationship betw...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00170-8