https://github.com/lysxia/cfpt
Counting Functional Pregroup Types
https://github.com/lysxia/cfpt
Last synced: 7 months ago
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Counting Functional Pregroup Types
- Host: GitHub
- URL: https://github.com/lysxia/cfpt
- Owner: Lysxia
- Created: 2014-05-01T13:40:16.000Z (about 12 years ago)
- Default Branch: master
- Last Pushed: 2014-05-07T12:04:57.000Z (about 12 years ago)
- Last Synced: 2025-04-24T00:57:52.795Z (about 1 year ago)
- Language: Haskell
- Size: 133 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
Counting Functional Pregroup Types
===
_Short version_:
We consider words on the set `Z` of relative integers.
In particular, `X` is the smallest set such that
1. It contains the one-letter word `0`.
2. If `a` and `b` are two words of `X`,
then `X` also contains `a L(b)` and `R(a) b`.
`L(a)` is obtained by taking the reverse of `a`
and subtracting one to every letter.
`R(b)` is obtained by taking the reverse of `b`
and adding one to every letter.
---
Find the number `X(n)` of words of length `n`.
---
*Conjecture*: `X(n) = sum(i = 0 .. n, C(2 * n - i, n + i))`.
`C(n, k)` is the binomial coefficient.
http://oeis.org/A108081