# Short notation for Turing machine configurations

I'm writing about Turing machines and often need to denote the tape. I'm using exponential tapes, i.e. a repetition count for each symbol.

I usually use something similar to $(x_k^{e_k})_{1 \leq k \leq m} \text{ Q } (x_k^{e_k})_{m+1 \leq k \leq n}$ (latex: $(x_k^{e_k})_{1 \leq k \leq m} \text{ Q } (x_k^{e_k})_{m+1 \leq k \leq n}$) with $x_k$ the symbols and $e_k$ their exponents. The head in state $Q$ is at position $m$.

What (very slightly) annoys me about this is the need to include $Q$. Without it, it would just be $(x_k^{e_k})_{1 \leq k \leq n}$ (latex: $(x_k^{e_k})_{1 \leq k \leq n}$) , which is must easier to read.

The transitions may change various symbols and exponents at the same time, while $Q$ almost always stays in the same spot.

How should I note this down? Is there an easy to understand (and parse) notation which is shorter but still carries the same information? I could not find a solution in the papers I read. Or maybe I should just carry on, because this isn't an issue at all?

This is just a convention. You can write a configuration as the tuple that has the same information. Eg, a possible way to write a configuration is as the tuple $$Config= (tape,state,pos)$$
where $tape$ is the non empty tape content, $state$ is the current state, and $pos$ is the position of the head.