For example, if there are three candidates, and it is assumed that the voters' preferences are represented by linear orderings, then each linear ordering can occur with probability 1/6.
The theory Td, for example, of dense linear ordering (such as that of the rational numbers) is categorical in the countable cardinality.
An interval hypergraph is a hypergraph whose vertex set allows a linear ordering such that each edge is a set of consecutive vertices in this order.
In this paper, we describe the principles and the results of an exact method designed to solve the linear ordering problem for any weighted tournament.
However, instead of ordering by the degree function (Hall words), he used an arbitrary linear ordering of non-associative monomials satisfying ( ( u ) ( v ) ) > ( v ).
Mitchell and Borchers ([2000]) have noted that an exact solution to a linear ordering problem with 250 objects or sectors can be obtained.
It is possible to show that the set of those cuts can, in turn, be endowed with a linear ordering and with operations of addition and multiplication, thus constituting a totally new "number system".
These theories have the remarkable property that every infinite indiscernible sequence in any of their models is indiscernible under any linear ordering whatever; so these sequences are a kind of generalisation of bases of vector spaces.
In the following, we always suppose that E is a real Banach space endowed with a cone P with the apex at the origin 0 E, int ( P ) ≠ ∅ and a linear ordering ≤ E with respect to P. Definition 2.8 ([14]).
The criterion of success in this task which is employed here is one of coherence: a good account should accommodate all of Wittgenstein's remarks in §§244 271, their (not necessarily linear) ordering as well as their content, and should make clear how these remarks fit with the context provided by the rest of the book.
Formally, this requires the existence of a linear ordering Ω on X such that, for every triple of alternatives x, y, z ∈ X, if y lies between x and z with respect to Ω, it is not the case that xRiy and zRix (this rules out a 'cave' between x and z, at y). Single-peakedness is plausible in some democratic contexts.
