  We have witnessed an impressive advancement in computer performance in the
last couple of decades. One would therefore expect a trickling down of the
benefits of this technological advancement to the borough of computational
simulation of multispin magnetic resonance spectra, but that has not been quite
the case. Though some significant progress has been made, chiefly by Kuprov and
collaborators, one cannot help but observe that there is still much to be done.
In our view, the difficulties are not to be entirely ascribed to technology,
but, rather, may mostly stem from the inadequacy of the conventional
theoretical tools commonly used. We introduce in this paper a set of
theoretical tools which can be employed in the description and efficient
simulation of multispin magnetic resonance spectra. The so-called
Holstein-Primakoff transformation lies at the heart of these, and provides a
very close connection to discrete mathematics (from graph theory to number
theory). The aim of this paper is to provide a reasonably comprehensive and
easy-to-understand introduction to the Holstein-Primakoff (HP) transformation
(and related bosons) to researchers and students working in the field of
magnetic resonance. We also focus on how through the use of the HP
transformation, we can reformulate many challenging computing problems
encountered in multispin systems as enumerative combinatoric problems. This,
one could say, is the HP transformation's primary forte. As a matter of
illustration, our main concern here will be on the use of the HP bosons to
characterize and eigendecompose a class of multispin Hamiltonians often
employed in high-resolution magnetic resonance.
