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Polytope Projects
book

Polytope Projects

by Octavian Iordache
October 2013
Intermediate to advanced content levelIntermediate to advanced
236 pages
6h 11m
English
CRC Press
Content preview from Polytope Projects
22 Polytope Projects
The set P
n
={x: ρ(x) = n
Z} are called levels of G.
G can be regarded either as oriented or non-oriented graph. The
accessibility relation in an oriented graph defi nes a partial order on P. If
there are no multiple arcs, G is the Hasse diagram of this poset. The paths
in non-oriented graphs are the Hasse walks.
As for the differential posets the “down” and “up” operators can be
defi ned.
Let G= (P, ρ, E) be a graded graph. Linear operators U and D are defi ned
by:
=
E)y,x(
y)y,x(mUx
;
=
E)y,x(
x)y,x(mDy
(2.5)
Here m (x, y) is the multiplicity of the edge (x, y) in E.
The main idea of Fomin was to consider the pairs of graded graphs
G
1
= (P, ρ, E
1
) and G
2
= (P, ρ, E
2
) with a common set of vertices and a common
rank function.
The oriented ...
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Publisher Resources

ISBN: 9781482204643