$q$-coefficient table of negative exponent polynomial with $q$-commuting variables
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Abstract
Let $N^{(q)}$ be an arithmetic table of a negative exponent polynomial with $q$-commuting variables. We study sequential properties of diagonal sums of $N^{(q)}$. We first device a $q$-coefficient table $\hat N$ of $N^{(q)}$, find sequences of diagonal sums over $\hat N$, and then retrieve the findings of $\hat N$ to $N^{(q)}$. We also explore recurrence rules of $s$-slope diagonal sums of $N^{(q)}$ with various $s$ and $q$.
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