Let P be a poset and let P* be the set of all finite length words over P.
Generalized subword order is the partial order on P* obtained by letting u \leq
w if and only if there is a subword u' of w having the same length as u such
that each element of u is less than or equal to the corresponding element of u'
in the partial order on P. Classical subword order arises when P is an
antichain, while letting P be a chain gives an order on compositions. For any
finite poset P, we give a simple formula for the Mobius function of P* in terms
of the Mobius function of P. This permits us to rederive in a easy and uniform
manner previous results of Bjorner, Sagan and Vatter, and Tomie. We are also
able to determine the homotopy type of all intervals in P* for any finite P of
rank at most 1.Comment: 29 pages, 4 figures. Incorporates referees' suggestions; to appear in
Advances in Mathematic
