Effect of compactness of notation on cognition?
If I recall correctly, in his book "The number sense", Stanislas Dehaene says that one reason Chinese have better than average math skills is because all digits have only 1 syllable and the number of syllables increases linearly with the number of digits (vs. for example the horrible seventy-seven in English). If I still remember correctly, he cites some studies about that. It's not exactly what you asked but that's definitively a reference relevant to your question.

Dehaene, S. (2011). The number sense: How the mind creates mathematics. OUP USA.