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Results tagged with co.combinatorics
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user 728
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
31
votes
3
answers
10k
views
Cutting a rectangle into an odd number of congruent non-rectangular pieces
We are interested in tiling a rectangle with copies of a single tile (rotations and reflections are allowed). This is very easy to do, by cutting the rectangle into smaller rectangles.
What happens wh …
- 1,110
15
votes
Cutting a rectangle into an odd number of congruent non-rectangular pieces
I am posting the 11 pieces solution shown in the article cited by Michael (it is not freely available online).
(source)
This is the smallest known number of pieces. Some remarks:
The question …
- 1,110
9
votes
Regular languages and the pumping lemma
Another good way to prove language L non-regular is to find a regular language A such that L∩A is non-regular.
For example, one can take A = a*b*, and prove that L∩A = {a^nb^n : n≥0}.
This method wo …
- 1,110