Chess tableaux (Q2570992)

A chess tableau is a standard Young tableaux, in which the \((i,j)\) entry is always congruent to \(i+j+1\) mod 2. Chess tableaux were introduced in two recent, independent papers. The paper enumerates \(3\times n\) chess tableaux. Their number agrees to the number of Baxter permutations of \(n-1\). This follows from a bijection between certain 3-row chess tableaux and certain 3-row Dulucq-Guibert nonconsecutive tableaux. Several open problems are included. There is an explanation how helpstalemate chess compositions motivate chess tableaux.