Trace Diagrams Collaboration Page

Estimated Submission: Spring Break 2009 (finish write up last 5%, troll out and edit manuscript, lastly smooth over rough spots)
Submitted: awaiting response

Elisha's Tasks
Re-read entire paper again
Fix rank three notations
Add in several more references on diagrams
Add preliminaries on diagrams, and basic examples
Respond to Sean's edits
Add discussion of signs
Explicit barbell computation
write diagramatically the rank 3 relation
Here is a place for your title Click me to edit ! false
Sean's Tasks
(1) add in section 1 edits
(2) add in section 2 edits
(3) add in section 6 edits
(4) make jarnal file edits on sections 3-5 (and where to add in diagrams elsewhere)
edit entire article (Monday 8/4)
discuss possilbe algorithms to compute reynolds graphically (decided to leave as comment only in this paper and possibly explore further at a later time)
Update with Jarnal edits
Add in Reynolds comment
add in shur like lemma comment
Figure out relevance to Reynolds Operator
add more documentation to public mathematica file (LOW PRIORITY)
update Wolfram library (LOW PRIORITY)
make note that program seems to not run appropriately in Mathematica 7 (better yet try to debug for mathematica 7)[low priority]
Prove (via spin networks) shur like lemma (CUT FOR NOW)
compute the reynolds operator in terms of spin networks in some examples (CUT FOR NOW)

Point Distribution Algorithm (edited by elishapetersonelishapeterson on 01 Mar 2010 18:41)
Trace Diagrams Collaboration Page (edited by Sean LawtonSean Lawton on 30 Nov 2009 15:21) (edited by elishapetersonelishapeterson on 09 Feb 2009 19:01)
nonsimplerecurrence.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 19:01)
simplerecurrence.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 19:00)
tracediagramreview.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 19:00)
rankrcentral.workingwiki.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 18:59)
spinnetsintro.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 18:59)
intro.workingwiki.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 18:57)
spinsl2-ii.workingwiki.tex (edited by elishapetersonelishapeterson on 09 Feb 2009 18:56)
Collaboration Pages (edited by elishapetersonelishapeterson on 07 Jul 2008 23:12)

TeX Links (working wiki pages)

  1. spinsl2-ii.workingwiki.tex
  2. intro.workingwiki.tex
  3. spinnetsintro.tex
  4. rankrcentral.workingwiki.tex
  5. tracediagramreview.tex
  6. simplerecurrence.tex
  7. nonsimplerecurrence.tex
  8. rank3.workingwiki.tex

Supporting Files

  1. tikzstyledefs.tex


  • Sean is working on at present.
  • Elisha is working on at present.

Publication Information

Outline (copied from PDF)

1. Introduction 2
2. Rank r Central Functions 2
3. Decompositions and Central Functions 2
4. Review of Trace Diagram Central Function Representation 2
4.1. Notation 2
4.2. Fundamental Spin Network Identities 2
4.3. Modifying Spin Network Identities 3
5. Simple Loop Recurrences 4
5.1. An Essential Lemma 4
5.2. The Main Result 5
5.3. Left Associative Central Function Recurrences 6
6. Non-Simple Loop Recurrences 8
6.1. A General Recurrence Formula 9
6.2. Barbell Recurrences 10
7. Rank Three Central Functions 11
7.1. Tensorial Algorithm 11
7.2. Combinatorial Algorithm 14
7.3. Computations 15
7.4. Shur Like Lemma 17
8. Symmetry and Central Functions 17
References 17


Elisha's Thesis
"Spin Networks and Character Varieties" paper
PGF/TikZ Manual (large!)
Goldman Paper


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