Permutations and Combinations mathematical puzzle

I am investigating permutations and combinations of the knight. Given that there are no other pieces on the board, and that the knight can make 2 moves, we can observe that there are 18 possibilities. Would this be permutations or combinations? and, what would be n and r? Also, if repetitions were not allowed, there would be 13 possibilities, how is this shown mathematically (i guess it is with the npr/x!)

Neither.

This is not pure math in a discrete math sense because the edge of the board creates a large complication that negates the meaning and utility of the usual formulas and variables.

Without edges to the board, there would be 64 possibilities, still neither a permutation nor a combination computation.

We're always talking in terms of what the knight can do. Has anyone ever asked the knight what it wants to do?

Without a specific example, I can not say much about your use of permutation and combination above.

As far as I can tell, LookingToPlayChess is not using permutation and combination in the usual mathematical sense.

well, if other assumptions were made, such as an  infinite board or a black pawn in e3, could the use of permutations/combinations be possible? Also, could i find some sort of sequence/series for the knight in any way? 

Thanks for the help lads

Nicksypilicksy seemed to me to want to discuss a "Permutations and Combinations mathematical puzzle".

It is difficult to say what is possible, especially without a specific problem. Suffice to say, you do not seem to me to be considering issues where the solution is given by choosing an n, choosing an r, and choosing a C or P. I doubt that it will help to choose an x and divide by x! . I see no likely value to thinking about sequences and series here. Of course, I am no Ramanujan or anything.

True.

There is only one object (one knight) that can go into various slots (squares of the board) so it can't be a permutation because order is not relevant (one object can't be ordered), and it can't be a combination because there is only one object to put into the slots.

https://betterexplained.com/articles/easy-permutations-and-combinations/

Also, the question is not one of distributing objects into slots, but rather a question of counting possible destinations under various constraints of motion type and the edge of the board. You also need to specify whether you intend to count multiple paths to the same destination as one count, or multiple counts.

To get a formula it would be easier to start with objects with simpler motions, like a rook, and in the center of a large board so that the edge does not have yet have an effect, and gradually increase the complexity of the motions, then finally consider edge effects.