Mutually Counting Sequences
Steven Kahan · The Fibonacci Quarterly · 1980
Let n and m be positive integers with n ≤ m. Let A be the sequence of n nonnegative integers a(0), a(1) , …, a(n - 1), and let B be the sequence of m nonnegative integers b(0), b(1), …, b(m - 1), where a(i) is the multiplicity of i in B and b(j) is the multiplicity of j in A. We prove that for n > 7, there are exactly 3 ways to generate such pairs of sequences.