bibkey: sabba2023a362534 authors: Mohamed Sabba year: 2023 title: “OEIS A362534, Numerators of the ratio of the symmetry-constrained bound to the adiabatic bound on polarization transfer in AXn spin-1/2 systems” doi: null url: https://oeis.org/A362534 claim: “The entry defines the symmetry-constrained bound f(n) and the adiabatic bound g(n) on z-magnetization transfer in AXn spin-1/2 systems, lists the numerators of f(n)/g(n), and conjectures that the numerator of g(n) is the denominator of f(n)/g(n).” strata_touched:

• D5/S0/Certificates/SabbaPolarizationTransferRefutation license: citation-only triage: anchor

OEIS A362534

The NAME of A362534 states:

Numerators of the ratio of the symmetry-constrained bound to the adiabatic bound on polarization transfer in AXn spin-1/2 systems.

The COMMENTS place the numbers in NMR spin dynamics, as upper bounds on the transfer of z-magnetization from a group of spin-1/2 nuclei X_n to a single spin-1/2 nucleus A, and define

The symmetry-constrained upper bounds are given by the function f(n): (1) for even n, f(n) = (2^(1-n))nbinomial(n-1, n/2) (2) for odd n, f(n) = (2^(1-n))nbinomial(n-1, (n-1)/2) The adiabatic bounds are given by the function g(n): (3) for even n, g(n) = 2*(1-(2^(-n))binomial(n, n/2)) (4) for odd n, g(n) = 2(1-(2^(-n))*binomial(n, (n-1)/2))

together with a(n) = numerator(f(n)/g(n)), the first values g = 1, 1, 5/4, 5/4, 11/8, 11/8, 93/64, … and f/g = 1, 1, 6/5, 6/5, 15/11, 15/11, 140/93, …, all in lowest terms. The comments end with

Conjecture: the numerator of g(n) is the denominator of f(n)/g(n).

The entry cites Chingas, Garroway, Moniz and Bertrand (1980) for the adiabatic bounds, Sørensen (1990) for the symmetry-constrained bounds, and Levitt (2016).

Verified locator

• URL: https://oeis.org/A362534
• Version and location: OEIS A362534, revision 24 (2023-06-11), COMMENTS, items (1)–(6) and the closing conjecture; author Mohamed Sabba, 2023-04-24.