Normally a chess problem must have a unique solution, and is deemed unsound
even if there are alternatives that differ only in the order in which the same
moves are played. In an enumerative chess problem, the set of moves in the
solution is (usually) unique but the order is not, and the task is to count the
feasible permutations via an isomorphic problem in enumerative combinatorics.
Almost all enumerative chess problems have been ``series-movers'', in which one
side plays an uninterrupted series of moves, unanswered except possibly for one
move by the opponent at the end. This can be convenient for setting up
enumeration problems, but we show that other problem genres also lend
themselves to composing enumerative problems. Some of the resulting
enumerations cannot be shown (or have not yet been shown) in series-movers.
This article is based on a presentation given at the banquet in honor of
Richard Stanley's 60th birthday, and is dedicated to Stanley on this occasion.Comment: 14 pages, including many chess diagrams created with the Tutelaers
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