Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux

This work develops a theory for counting nonintersecting lattice paths by the major index and generalizations of it. As applications, Krattenthaler computes certain tableaux and plane partition generating functions. In particular, he derives refinements of the Bender-Knuth and McMahon conjectures, thereby giving new proofs of these conjectures. Providing refinements of famous results in plane partition theory, this work combines in an effective and nontrivial way classical tools from bijective combinatorics and the theory of special functions.Krattenthaler, C. is the author of 'Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux' with ISBN 9780821826133 and ISBN 0821826131.