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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.
2
votes
Number of solutions and minimal clues in Sixy Sudoku
As for the first question, a backtracking algorithm, see sixy.c at
https://github.com/wilberdk/sixy
shows there are 1936 completions of
$$\matrix{1&2&3&4&5&6\cr
*&*&*&*&*& *\cr
*&*&*&*&*&*\cr
*&*& …
53
votes
Conceptual reason why the sign of a permutation is well-defined?
Draw a braid on $n$ strings sloppily, so that no three strings pass through the same point. Convince yourself that the parity of the number of crossings is the same in every other drawing of the sam …