The algebra and combinatorics of shuffles and multiple zeta values

被引：31

作者：

Bowman, D

Bradley, DM

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Maine, Dept Math & Stat, Orono, ME 04469 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2002年 / 97卷 / 01期

关键词：

Lie algebra; shuffle; multiple zeta value; iterated integral;

D O I：

10.1006/jcta.2001.3194

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The algebraic and combinatorial theory of shuffles, introduced by Chen and Ree, is further developed and applied to the study of multiple zeta values. In particular, we establish evaluations for certain sums of cyclically generated multiple zeta values. The boundary case of our result reduces to a former conjecture of Zagier. (C) 2002 Elsevier Science.

引用

页码：43 / 61

页数：19

共 50 条

[1] Algebra structure of multiple zeta values in positive characteristic
Chang, Chieh-Yu
Chen, Yen-Tsung
Mishiba, Yoshinori
CAMBRIDGE JOURNAL OF MATHEMATICS, 2022, 10 (04) : 743 - 783
[2] Shuffle Products of a Single Zeta Value and Multiple Zeta Values of Height One With Applications in Combinatorics
Eie, Minking
Lee, Tung-Yang
Ong, Yao Lin
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2015, 39 (05) : 613 - 624
[3] SOME IDENTITIES IN THE HARMONIC ALGEBRA CONCERNED WITH MULTIPLE ZETA VALUES
Li, Zhong-Hua
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2013, 9 (03) : 783 - 798
[4] The algebra of generating functions for multiple divisor sums and applications to multiple zeta values
Henrik Bachmann
Ulf Kühn
The Ramanujan Journal, 2016, 40 : 605 - 648
[5] The algebra of generating functions for multiple divisor sums and applications to multiple zeta values
Bachmann, Henrik
Kuehn, Ulf
RAMANUJAN JOURNAL, 2016, 40 (03): : 605 - 648
[6] The Combinatorics of Biased Riffle Shuffles
Jason Fulman
Combinatorica, 1998, 18 : 173 - 184
[7] The combinatorics of biased riffle shuffles
Fulman, J
COMBINATORICA, 1998, 18 (02) : 173 - 184
[8] Relations between elliptic multiple zeta values and a special derivation algebra
Broedel, Johannes
Matthes, Nils
Schlotterer, Oliver
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (15)
[9] The algebra of cell-zeta values
Brown, Francis
Carr, Sarah
Schneps, Leila
COMPOSITIO MATHEMATICA, 2010, 146 (03) : 731 - 771
[10] FINITE MULTIPLE ZETA VALUES, SYMMETRICMULTIPLE ZETA VALUES AND UNIFIED MULTIPLE ZETA FUNCTIONS
Komori, Yasushi
TOHOKU MATHEMATICAL JOURNAL, 2021, 73 (02) : 221 - 255

← 1 2 3 4 5 →