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⇤ ← Revision 1 as of 2007-07-09 21:42:18
Size: 889
Comment:
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Size: 890
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 34: | Line 34: |
| w is a smoth permutation iff #{Tij <= w} = h(w) (i < j) | w is a smooth permutation iff #{Tij <= w} = h(w) (i < j) |
Notes that Tom took during meeting with Sara on Friday:
list of isomorphism classes of subintervals
hasse diagram partial interval
k-crowns: ranked degree sequences (and up vs. down)
Ekedahl (Ekedahl structure interval)
Kazhdan - Lusztig polynomial
Questions:
when is [id,v] ~ [id,w] ?
completely determined by heights & degrees?
count # interval isomorphism classes
1) [id,w]
2) all
Pattern avoidance:
(general idea)
for n = 1,2,3...
for all w \in Sn
if (has_property(w) == avoids_pattern(w)):
'good'
else
print has_property(w), avoids_patterns(w)
add w to known patterns
(specific examples)
Smoothness:
w is a smooth permutation iff #{Tij <= w} = h(w) (i < j)
3412 or 4231 avoiding
Fully commutative perms: w avoids 321