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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.

Proves Rivoal's 'denominator conjecture' concerning the common denominators of coefficients of certain linear forms in zeta values; these forms were constructed to obtain lower bounds for the dimension of the vector space over $mathbb Q$ spanned by $1,zeta

This volume contains the proceedings of the International Conference on Number Theory and Discrete Mathematics in honour of Srinivasa Ramanujan, held at the Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India, in October 2000, as a contribution to the International Year of Mathematics. It collects 29 articles written by some of the leading specialists worldwide. Most of the papers provide recent trends, problems and their current states as well as historical backgrounds of their subjects. Some contributions are related to Ramanujan's mathematics, which should...