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Results tagged with co.combinatorics
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user 18702
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Product of $q$-analogues
Background
Recall that the $q$-analogue $[n]_q\in\mathbb Z[q]$ of a natural number $n\in\mathbb N$ is defined as
$$ [n]_q := \frac{q^n -1}{q-1}$$
the idea being that formulas involving $q$ will speci …
- 1,838
2
votes
Accepted
Product of $q$-analogues
Recall Legendre's formula
$$ v_p(n!) = \sum_{s=1}^\infty\left\lfloor\frac n{p^s}\right\rfloor = \sum_{r=0}^\infty a_r[r]_p $$
where $n = \sum a_r p^r$ is the base-$p$ expansion of $n$.
A $q$-analogu …
- 1,838