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 [10] and the author’s [5] 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 [5] to q-quasi-polynomials.