Asymptotics of the Number of Restricted Partitions
Tóm tắt
Let
$$00$$
. For any
$$T>0$$
and
$$k\in\overline{\mathbb{N}}=\mathbb{N}\cup\{\infty\}$$
, let
$$N(k,T)$$
be the number of solutions
$$\{n_j\}_{j=1}^k$$
,
$$n_j\in \mathbb{N}_0=\mathbb{N}\cup\{0\}$$
, of the inequality
$$\sum_{j=1}^{k}n_jt_j\le T$$
. We are interested in the asymptotics of
$$\log N(k,T)$$
as
$$T\to\infty$$
.
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