#20555: descents for Permutations : cleanup
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Reporter: | Owner:
chapoton | Status: needs_review
Type: | Milestone: sage-7.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
permutation | e6393ab4a5bc9917a95a7e472452548eeed33ddd
Authors: | Stopgaps:
Frédéric Chapoton |
Report Upstream: N/A |
Branch: |
u/chapoton/20555 |
Dependencies: |
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Comment (by stumpc5):
I am personally not totally convinced that this change is the right way to
go - I think it is a typical example that it is simply very hard to make
notions that are consistent all over math:
1. Let w be a finite word in a totally ordered alphabet,say {1,...,n}. Its
descents are the positions i such that w_i > w_{i+1}. Since python indexes
words (or rather lists/tuples) starting with 0, it is natural to write w =
w_0 w_1 ... w_m.
2. Let w be a permutation of {1,...,n}. A descent of w is an index i such
that w*(i i+1) ls weak order smaller than w. But on the other hand, its
one-line notation is a word, it inherits the notion of descents from
above, which now differs in a shift by 1.
(There are tons of other examples already in the combinatorics part of
sage, and the category framework makes that *really* hard to properly
organize imho.)
--
Ticket URL: <http://trac.sagemath.org/ticket/20555#comment:7>
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