These operations, along with the related constructions of intervals and covering maps, mean that questions about cyclic orders can often be transformed into questions about linear orders.
32.
According to, Bach had a clear liturgical purpose in his organ compendium, with its cyclic order and plan, clear to the eye if not the ear.
33.
In the torus embedding of this dual graph, the six edges incident to each vertex, in cyclic order around that vertex, cycle twice through the three other vertices.
34.
Since a linear order induces a cyclic order, cyclically ordered groups are also a generalization of linearly ordered groups : the rational numbers, the real numbers, and so on.
35.
This relation is a partial cyclic order, but it cannot be extended with either " abc " or " cba "; either attempt would result in a contradiction.
36.
Hubard Escalera began her studies in the Faculty of Sciences of the UNAM, where in 2001, she graduated in Mathematics with a baccalaureate thesis titled " Polyhedra colored with cyclic orders ".
37.
Consider a finite set that is linearly ordered, or ( equivalently, for purposes of this definition ) arranged in a cyclic order like the vertices of a regular " n "-gon.
38.
Its sequent calculus relies on the structure of order varieties ( a family of cyclic orders which may be viewed as a species of structure ), and the correctness criterion for its proof nets is given in terms of partial permutations.
39.
So now look at those five vertices v _ 1, v _ 2, v _ 3, v _ 4, v _ 5 that were adjacent to v in cyclic order ( which depends on how we write G ).
40.
Equivalently, the vertices of every 2-vertex-connected graph " G " may be arranged into a cyclic order such that adjacent vertices in this order are at distance at most two from each other in " G ".
