@Alex #38
So Puzzle 12 would be \(\lfloor\frac{n}{2}\rfloor\) and Puzzle 13 would be \(\lfloor\frac{n+1}{2}\rfloor\). Am I crazy?
I get a different form of the answer to Puzzle 13: \(g(n) = \lceil \frac{n}{2} \rceil\). But \( \lfloor \frac{n+1…
I'm afraid I'm still confused about the answers to puzzles 12 and 13 that are re-quoted here in the lecture material - I get a right adjoint \(g(n) = \lfloor n/2 \rfloor \), not \( \lceil n/2 \rceil\) as is given in the lecture. Or (much less likely…
Thanks Patrick and Thomas, your question clarified puzzle 11 for me also.
Patrick, regarding puzzles 12 and 13, I think the answers you gave are indeed adjoints but flipped (right -> left, left -> right). For example, take m=2, n=3 for puzzle…
Hi Alfredo,
What kind of theoretical physics problems are you interested in for graduate work? I'm about to finish my PhD program in nuclear physics and I also found statistical mechanics deeply satisfying - one of the reasons I wound up in a gradu…
Hi Derrick, Dan, John,
Yep, the film is The Surrounding Game (thanks for linking, Dan). The film follows some of the strongest players in North America as they try to become the first Western professional players set against the backdrop of Go in A…
Dan, I agree: as far as I can tell, it hinges on the compelled move question with respect to the only non-reversible piece (pawn), and/or whether 0 legal moves is included in the definition of \(\leq\). I think if pawns are all removed from the boar…
How about the set of all legal chess positions as a preorder? In this case, \(\leq\) is interpreted as "can produce by legal moves".
This doesn't seem partially ordered, though, because cycles are possible: I can move a bishop back and forth to rep…