Constructive families and an extension theorem for binary permutation X-rays
We prove permutation realization for every admissible binary X-ray profile whose rank deviations from the odd staircase lie in [-2, 2], at every order and without a bound on density slack. We also prove the one-sided families with all deviations at least -1 or all deviations at most 1, with at least 2^u realizations, where u counts positive or negative deviations respectively. For n >= 1, if a label multiset L is realizable at order n, then Q(L) = {3, 2n+1} multiset-union (L+2) is realizable at order n+2. If every source label lies in [2, 2n-2], then h(L) <= h(Q(L)), where h counts…
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