Polynomial $f(x_1, …, x_n, y_1, …, y_m)$?

Question

In publication abstract we have:

Given a polynomial $f(x_1, …, x_n, y_1, …, y_m)$ with integer coefficients ...

What is the meaning of this polynomial?

This can be: $x_1^{y_1} + x_2^{y_2} + x_2^{y_2} = x_3^{y_3}$ ($n=3$ and $m=3$)?

Answer 1

It would be of the form $\sum a_{i_{1},..,i_{n},j_{1},...,j_{m}}x_{1}^{i_{1}}...x_{n}^{i_{n}}y_{1}^{j_{1}}...y_{m}^{j_{m}}$ where each of the coefficients $a_{i_{1},...,i_{n},j_{1},...,j_{m}}$ are integers.