  Zeckendorf proved that any integer can be decomposed uniquely as a sum of
non-adjacent Fibonacci numbers, $F_n$. Using continued fractions, Lekkerkerker
proved the average number of summands of an $m \in [F_n, F_{n+1})$ is
essentially $n/(\varphi^2 +1)$, with $\varphi$ the golden ratio. Miller-Wang
generalized this by adopting a combinatorial perspective, proving that for any
positive linear recurrence the number of summands in decompositions for
integers in $[G_n, G_{n+1})$ converges to a Gaussian distribution. We prove the
probability of a gap larger than the recurrence length converges to decaying
geometrically, and that the distribution of the smaller gaps depends in a
computable way on the coefficients of the recurrence. These results hold both
for the average over all $m \in [G_n, G_{n+1})$, as well as holding almost
surely for the gap measure associated to individual $m$. The techniques can
also be used to determine the distribution of the longest gap between summands,
which we prove is similar to the distribution of the longest gap between heads
in tosses of a biased coin. It is a double exponential strongly concentrated
about the mean, and is on the order of $\log n$ with computable constants
depending on the recurrence.
