Enumeration of skew Ferrers diagrams and basic Bessel functions (Q1209643)

This is a survey paper on the enumeration of skew Ferrers diagrams according to their area and number of columns. The generating function for the problem \[ F(t;q)={\sum^ \infty_{n=0}((-1)^ nq^{{n+1\choose 2}}/(q;q)_ n(q;q)_{n+1})q^{n+1}t^{n+1}\over\sum^ \infty_{n=0}((-1)^ nq^{{n\choose 2}}/(q;q)^ 2_ n)q^ nt^ n}, \] where \((a;q)_ n=(1-a)(1-aq)(1-aq^ 2)\cdots(1-aq^{n-1})\), is related to the quotient of two basic Bessel functions. The combinatorial theories in the background are the \(q\)-analogue of the Schützenberger method, the enumeration of multichains in posets, and the Ehrhart theory of enumeration of integer points in a polytope.