Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions

Relations between the mean values of distributions flipped spins on periodic Heisenberg XX chain and some aspects enumerative combinatorics are discussed. The Bethe vectors, which state-vectors model, considered both as on- off-shell. It is this approach that makes it possible to represent study correlation functions in form non-intersecting nests lattice walks related plane partitions. We distinguish two types walkers, namely lock step models random turns. Of particular interest connection turns a circulant matrix. determinantal representation for norm-trace generating function partitions with fixed height diagonal parts obtained expectation exponential over off-shell N-particle states. asymptotics dynamical value calculated double scaling limit provided evolution parameter large. shown amplitudes leading depend number diagonally constrained