  The mean values of non-homogeneously parameterized generating exponential are
obtained and investigated for the periodic Heisenberg XX model. The norm-trace
generating function of boxed plane partitions with fixed volume of their
diagonal parts is obtained as N-particles average of the generating
exponential. The generating function of self-avoiding walks of random turns
vicious walkers is obtained in terms of the circulant matrices that leads to
generalizations of the Ramus's identity. Under various specifications of the
generating exponential, the N-particles averages arise for a set of
inconsecutive flipped spins and for powers of the first moment of flipped spins
distribution at large length of the chain. These averages are expressed through
the numbers of closed trajectories with constrained initial/final positions.
The estimates at large temporal parameter are expressed through the numbers of
diagonally restricted plane partitions characterized by fixed values of the
main diagonal trace or by fixed heights of the diagonal columns in one-to-one
correspondence with the flipped spins positions.
