Use this tag for questions pretaining to q-analogs of functions, for example q-Binomials, $q$-derivatives, the q-theta function, the q-Pochammer symbol, etc.

learn more… | top users | synonyms

7
votes
0answers
158 views

Different notions of q-numbers

It seems that most of the literature dealing with q-analogs defines q-numbers according to $$[n]_q\equiv \frac{q^n-1}{q-1}.$$ Even Mathematica uses this definition: with the built-in function QGamma ...
4
votes
0answers
117 views

Example of something easier to count with $q$-analog?

Are there any known examples of combinatorial objects that become easier to count by considering some kind of $q$-analog? It seems to me that it might be impossible for the problem of computing the ...
4
votes
0answers
95 views

A general Combinatorics problem (Coefficients of the q factorial)

I was solving a combinatorics problem when I encountered difficulties. The problem was: $x_1 \in \{0,1\}$ $x_2 \in \{0,1,2\}$ . . $x_{n-1}\in\{0,1,2..,n-1\}$ We have to find the number of ways ...
4
votes
0answers
56 views

Necessary and sufficient condition for $f(q^n)$ to be in $\mathbb{Z}[q,q^{-1}]$ when $f\in\mathbb{Q}(q)[x]$?

In this question, user bgins shows that for each $k$ there is a unique polynomial $P_k(x)$ of degree $k$ whose coefficients are in $\mathbb{Q}(q)$, the field of rational functions, such that ...