Christian Krattenthaler's Books

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

By: Christian Krattenthaler

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

By: Christian Krattenthaler

A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.

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Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826131

ISBN 13

9780821826133

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

By: Christian Krattenthaler

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

By: Christian Krattenthaler

Average ratings

N/A

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Solve jigsaw puzzle

Age

Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826131

ISBN 13

9780821826133

"Jesus Is Victor!"

The Significance of the Blumhardts for the Theology of Karl Barth

By: Christian T. Collins Winn

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"Jesus Is Victor!"

The Significance of the Blumhardts for the Theology of Karl Barth

By: Christian T. Collins Winn

IN THIS INNOVATIVE WORK, Christian T. Collins Winn examines the role played by the Pietist pastors Johann Christoph Blumhardt (1805-1880) and Christoph Friedrich Blumhardt (1842-1919) in the development of Karl Barth's theology. The disparate theological themes and dynamics of the two Blumhardts were crystallized in their eschatology, and Collins Winn argues that as early as 1916 Barth had appropriated this "Blumhardtian eschatological deposit" in ways fundamental to his own theological development. Against the grain of current Barth scholarship, this book establishes how the theology of the Blumhardts, though critically reconstructed, was not merely an episodic influence on Barth's work. Instead, the Blumhardts had a complex and enduring impact on Barth, such that their imprint can be detected even in the mature theology of his Church Dogmatics. In treading new ground into Barth's theological formation, Jesus Is Victor! represents an important contribution to the field of Barth studies.

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Page Count

317

Publisher

Wipf and Stock Publishers

Published Date

ISBN 10

1630878294

ISBN 13

9781630878290

Book's by Christian Krattenthaler

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

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

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

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

"Jesus Is Victor!"

"Jesus Is Victor!"

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