Av(1243, 1324, 1342, 2143, 2314, 2431, 3142, 3241, 4123, 4132)

Permutation examples

length 2: 12, 21

length 3: 123, 132, 213, 231, 312, 321

length 4: 1234, 1423, 1432, 2134, 2341, 2413, 3124, 3214, 3412, 3421, 4213, 4231, 4312, 4321

length 5: 12345, 15423, 15432, 21345, 23451, 31245, 32145, 34512, 34521, 35214, 42135, 43125, 43215, 45213, 45231, 45312, 45321, 53214, 53412, 53421, 54213, 54231, 54312, 54321

Conjectured Struct Cover

$\mathcal{A}$
$=$
$\bullet$
$\bullet$
$\bullet$
\
$\bigsqcup$
$\bullet$
/
$\bullet$
\ $\bullet$
$\bigsqcup$
$\bullet$
/
$\mathcal{B}$
$\bullet$
\
$\bigsqcup$
$\bullet$
\
$\bullet$
$\bullet$
$\bullet$
$\bigsqcup$
/

Legend

$\mathcal{/}$ = Av(21)

$\mathcal{\setminus}$ = Av(12)

$\mathcal{A}$ = Av(1243, 1324, 1342, 2143, 2314, 2431, 3142, 3241, 4123, 4132)

$\mathcal{B}$ = Av(123, 132, 213)

Recurrence relation

$a_{0} = 1,~a_{1} = 1,~a_{2} = 2,~a_{3} = 6,~a_{4} = 14$

$a_{n} = \sum_{i=0}^{n-3}\binom{n-j-2}{1}+\sum_{i=0}^{n-2}\sum_{j=0}^{n-i-2}b_{n-i-j-2}+4$