Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux.

Intro -- Contents -- I. Introduction -- II. Definitions and Preliminaries -- 2.1 Definitions and Notation -- 2.2 Two involutions and nonintersecting lattice paths -- III. Counting by Major Index -- 3.1 Without restrictions -- 3.2 With a diagonal boundary -- 3.3 Tableaux generating functions -- IV. Counting by Strange Major Index -- 4.1 Without restrictions -- 4.2 With a diagonal boundary -- 4.3 Tableaux generating functions -- V. Detailed Proofs and Auxiliary Results -- 5.1 The major index and strange major index generating functions for lattice paths without restrictions -- 5.2 A correspondence for lattice paths that cross the line x = y -- 5.3 A correspondence for pairs of intersecting lattice paths -- 5.4 Correspondences between tableaux and nonintersecting lattice paths -- 5.5 A determinant lemma -- 5.6 A multiple basic hypergeometric summation -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.