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The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux
C. Krattenthaler
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Memoirs of the American Mathematical Society
1995; 109 pp; softcover
Volume: 115
ISBN-10: 0-8218-2613-1
ISBN-13: 978-0-8218-2613-3
List Price: US$41
Individual Members: US$24.60
Institutional Members: US$32.80
Order Code: MEMO/115/552
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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.

Readership

Researchers in enumerative and algebraic combinatorics.

Table of Contents

  • Introduction
  • Definitions and preliminaries
  • Counting by major index
  • Counting by strange major index
  • Detailed proofs and auxiliary results
  • References
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