Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Submit feedback
Contribute to GitLab
Switch to GitLab Next
Sign in / Register
Toggle navigation
V
veerer
Project overview
Project overview
Details
Activity
Releases
Cycle Analytics
Insights
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Locked Files
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Charts
Security & Compliance
Security & Compliance
Dependency List
Packages
Packages
List
Container Registry
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Charts
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Vincent Delecroix
veerer
Commits
e77549a2
Commit
e77549a2
authored
Sep 07, 2018
by
Saul Schleimer
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Added discussion of dimension.
parent
6447ee8a
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
32 additions
and
1 deletion
+32
-1
diary.txt
diary.txt
+32
-1
No files found.
diary.txt
View file @
e77549a2
2018-09-07 - or a few days earlier
2018-09-07
Note that there are easy upper bounds on the number of facets
(codimension one faces) of the core and geometric polytopes. To see
this: Cut down the parameter space using the equalities, to get a
single linear subspace of some dimension. If the triangulation is
core then this dimension is already the stratum dimension (as all
variables can be positive). Now cut down using the positivity
constraints - we get at most one facet for every positivity
constraint. Thus the number of facets of the core polytope is at most
twice the number of edges: 12g - 12 + 6p.
[This should be reduced to the number of small branches in the
vertical track plus the number of small branches in the horizontal
track, as the positivity of one of these implies positivity of the
edges "downstream" until the sink. Experiments show that there can be
dependencies between small branches, so the number of faces can be
smaller even smaller... ]
The geometric polytope is the same dimension (by assumption!) so the
number of additional facets is at most the number of flippable edges
(forward or backward). This is at most two-thirds the number of
edges, so we get 4g - 4 + 2p more giving an upper bound of
16g - 16 + 8p
faces. Note that the Keane faces where already counted previously,
and all faces are either Keane or Delaunay. Note furthermore that the
number of faces of any linear subspace intersected with the geometric
polytope has at most this number of facets as well.
2018-09-04 - or a few days earlier
1. Compute the shape of the octagon surface. Guess the linear space.
Check it has the correct dimension. Carry it around and see if the
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment