\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
\nopagenumbers
\noindent
%
%
{\bf Timothy Y. Chow, Henrik Eriksson and C. Kenneth Fan}
%
%
\medskip
\noindent
%
%
{\bf Chess Tableaux}
%
%
\vskip 5mm
\noindent
%
%
%
%
A {\it chess tableau\/} is a standard Young tableau in which, for all
$i$ and~$j$, the parity of the entry in cell $(i,j)$ equals the parity
of $i+j+1$. Chess tableaux were first defined by Jonas Sj\"ostrand in
his study of the sign-imbalance of certain posets, and were
independently rediscovered by the authors less than a year later in
the completely different context of composing chess problems with
interesting enumerative properties. We prove that the number of
$3\times n$ chess tableaux equals the number of Baxter permutations of
$n-1$, as a corollary of a more general correspondence between certain
three-rowed chess tableaux and certain three-rowed Dulucq-Guibert
nonconsecutive tableaux. The correspondence itself is proved by means
of an explicit bijection. We also outline how lattice paths, or rat
races, can be used to obtain generating functions for chess tableaux.
We conclude by explaining the connection to chess problems, and
raising some unanswered questions, e.g., there are striking numerical
coincidences between chess tableaux and the Charney-Davis statistic;
is there a combinatorial explanation?
\bye