The Algebra and Combinatorics of Shuffles andMultiple Zeta Values

2002/01/01 by Douglas Bowman, David M. Bradley · 6 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.CO #math.NT #msc:05E99 #msc:20F40 #msc:68R15

paper · pdf · doi:10.1006/jcta.2001.3194

published as Journal of Combinatorial Theory, Series A, Vol. 97 (2002), no. 1, pp. 43-61. MR1879045 (2003j:05010) · 21 pages, available online at http://www.idealibrary.com

openalex publication_date 2002/01/01 · arxiv created 2003/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the exponential solution of differential equations for a linear operator

Cited by

• Multiple q-zeta values
• Duality for finite multiple harmonic q-series
• Signed q-analogs of Tornheim's double series
• THIRTY-TWO GOLDBACH VARIATIONS
• Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
• Algebraic relations between harmonic sums and associated quantities