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Theory of multiple zeta values with applications in combinatorics / Minking Eie.

By: Material type: TextTextSeries: Monographs in number theory ; v 7.Publication details: Singapore : World Scientific, c2013.Description: xii, 300 p. : illustrations ; 24 cmISBN:
  • 9789814472630 (hardback)
Subject(s): DDC classification:
  • 515.56 23 Ei34
Contents:
1. Introduction to the theory of multiple zeta values -- 2. The sum formula -- 3. Some shuffle relations -- 4. Euler decomposition theorem -- 5. Multiple zeta values of height two -- 6. Generalizations of Pascal identity -- 7. Combinatorial identities of convolution type -- 8. Vector versions of some combinatorial identities -- Appendices-- Bibliography-- Index.
Abstract: This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory --
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Includes bibliographical references (pages 295-297) and index.

1. Introduction to the theory of multiple zeta values --
2. The sum formula --
3. Some shuffle relations --
4. Euler decomposition theorem --
5. Multiple zeta values of height two --
6. Generalizations of Pascal identity --
7. Combinatorial identities of convolution type --
8. Vector versions of some combinatorial identities -- Appendices--

Bibliography--
Index.

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory --

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