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on Stanley–Wilf limit for the permutation pattern $1324$ ($C_{30}$)

The statement

Let $\mathrm{Av}_n(1324)$ be the set of permutations of $\{1,2,\dots,n\}$ that avoid the permutation pattern $1324$ , and let

S_n(1324) := |\mathrm{Av}_n(1324)|.

[CJS12-def-Sn]

The Stanley–Wilf limit (growth constant) for the pattern $1324$ is

C_{30} \;:=\; \lim_{n\to\infty} \bigl(S_n(1324)\bigr)^{1/n}.

[CJS12-def-Ltau]

Equivalently, $C_{30} = \mathrm{gr}(\mathrm{Av}(1324))$ , the growth rate of the permutation class avoiding $1324$ .

[BBEPP2017-def-gr]

This limit is known to exist (and to be finite) for every fixed pattern, as a consequence of Marcus–Tardos and Arratia.

[CJS12-mt-expbound] [CJS12-arratia-exists]

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.