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To my knowledge, x, y, and z refer to the different electron pairs possible in orbital. There can be 2 electrons per orbital as long as they have opposite spin. In p, for example, there can be up to 6 electrons grouped in twos. To organize them we separate them by Px, Py, and Pz.
The only time to expand into the descriptive x, y, and z is when it is specified in the question or asked for. Otherwise, I believe it is fine to leave the configuration in its simplified form (no x, y, z). The x, y, and z are not necessarily part of the 4 main quantum numbers.
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