Another refinement of the Bender–Knuth (ex-)conjecture

We compute the generating function of column-strict plane partitions with parts in { 1 , 2 , … , n } , at most c columns, p rows of odd length and k parts equal to n . This refines both Krattenthaler’s [C. Krattenthaler, The major counting of nonintersecting lattice paths and generating functions for tableaux, Mem. Amer. Math. Soc. 115 (552) (1995) vi+109] and the author’s [I. Fischer, A method for proving polynomial enumeration formulas, J. Combin. Theory Ser. A (in press). Preprint, math.CO/0301103] refinement of the Bender–Knuth (ex-)conjecture. The result is proved by an extension of the method for proving polynomial enumeration formulas which was introduced by the author in I. Fischer [A method for proving polynomial enumeration formulas, J. Combin. Theory Ser. A (in press). Preprint, math.CO/0301103] to q -quasi-polynomials.