cp's OEIS Frontend

This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.

This is a rare example of Catalan Automorphism (with simple definition) where the cycle count sequence (A089411) is not monotone. (See A127296 for more complex example.)

This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.

This is a rare example of a simply defined Catalan Automorphism where the cycle count sequence (A089411) is not monotone. (See A127296 for a much more complex example.)

This is otherwise like A127291, but uses A127285 instead of A127287 as a "picker permutation" for the function "tau", which can be found in the entry A127291. A014486->parenthesization is given in A014486. This permutation contains some exceptionally large cycles, see A127297.

Note that a(12)/A000108(12) = 207882/208012 = 0.9994..., i.e. one orbit visits over 99.9% percent of all the Cat(12) structures of size 12, leaving only 208012 - 207882 = 130 structures for other A127296(12)-1 = 9 cycles. Cf. A127298.