  We define a notion of rank for words and subshifts that we call spacer rank,
extending the notion of rank-one symbolic shifts of Gao and Hill. We construct
infinite words of each finite spacer rank, of unbounded spacer rank, and show
there exist words that do not have a spacer rank construction. We consider
words that are fixed points of substitutions and give explicit conditions for
the word to have an at most spacer rank two construction, and not to be rank
one. We prove that finite spacer rank subshifts have topological entropy zero,
and that there are zero entropy subshifts not defined by a word with a finite
spacer rank construction. We also study shift systems associated with infinite
words, including those associated to Sturmian sequences, which we show are
spacer rank-two systems.
