Maximal avoidance conjecture for the patterns $M_{2m-1}$ and $M_{2m}$

Let $S_n(q)$ denote the number of permutations of length $n$ that avoid a pattern $q$. For $m\geq 2$, define $M_{2m}$ to be the pattern $132\cdots(2m-1)(2m-2)2m$, and define $M_{2m-1}$ to be the pattern obtained from $M_{2m}$ by removing its first entry and relabeling; thus $M_{2m-1}=21\cdots(2m-2)(2m-3)(2m-1)$. Maximal-$M$ conjecture. For every $m\geq 2$, both of the following hold: (A) for every positive integer $n$ and every pattern $q$ of length $2m-1$,

$$S_n(q)\leq S_n(M_{2m-1});$$

and (B) for every positive integer $n$ and every pattern $q$ of length $2m$,

$$S_n(q)\leq S_n(M_{2m}).$$

This is a stronger, parity-specific version supported by numerical evidence of the conjecture that layered patterns maximize the number of avoiding permutations. Its general validity remains open.