Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux.
Krattenthaler, C.
Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux. - 1st ed. - 1 online resource (122 pages) - Memoirs of the American Mathematical Society ; v.115 . - Memoirs of the American Mathematical Society .
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.
9781470401313
Generating functions.
Lattice paths.
Young tableaux.
Hypergeometric series.
Electronic books.
QA164.8 -- .K738 1995eb
511/.62
Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux. - 1st ed. - 1 online resource (122 pages) - Memoirs of the American Mathematical Society ; v.115 . - Memoirs of the American Mathematical Society .
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.
9781470401313
Generating functions.
Lattice paths.
Young tableaux.
Hypergeometric series.
Electronic books.
QA164.8 -- .K738 1995eb
511/.62