On the existence of Hamiltonian paths in the cover graph of M(n)

@article{Savage2003OnTE,
title={On the existence of Hamiltonian paths in the cover graph of M(n)},
author={Carla D. Savage and Ian Shields and Douglas B. West},
journal={Discrete Mathematics},
year={2003},
volume={262},
pages={241-252}
}

The poset M(n) has as its elements the n-tuples of integers a = (a1, a2, . . . , an) satisfying 0 = a1 = · · · = aj < aj+1 < · · · an ≤ n for some j, 0 ≤ j ≤ n. The order relation is defined by a ≤ b iff ai ≤ bi for 1 ≤ i ≤ n. We show that the cover graph of M(n) has a Hamiltonian path if and only if ( n+1 2 ) is odd and n 6= 5.