Binary-coset reversal and transposon growth

Establish the conjectured coincidence of reversal and transposon growth on binary Schreier cosets and prove the stated formulas for their layer sizes, God's number, modes, moments, antipodes, and limiting Gaussian behavior.

Background

The authors study Schreier graphs obtained from binary strings with floor(n/2) zeros and the remaining entries equal to one. They conjecture a detailed common description of the growth for reversal and transposon generators, including explicit binomial formulas and asymptotic statistical properties.

References

For binary cosets above:

— CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)  (2509.19162 - Chervov et al., 23 Sep 2025) in Section 15, subsection “Growth of Reversals and Transposons on binary cosets”