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Arborified multiple zeta values
- Source :
- Periods in Quantum Field Theory and Arithmetic, Jose Ignacio Burgos Gil, Kurusch Ebrahimi-Fard, Herbert Gangl. Periods in Quantum Field Theory and Arithmetic, 314, Springer, pp.469-481, 2020, Springer Proceedings in Mathematics & Statistics book series, 978-3-030-37030-5, Springer Proceedings in Mathematics & Statistics ISBN: 9783030370305
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- We describe some particular finite sums of multiple zeta values which arise from J. Ecalle's "arborification", a process which can be described as a surjective Hopf algebra morphism from the Hopf algebra of decorated rooted forests onto a Hopf algebra of shuffles or quasi-shuffles. This formalism holds for both the iterated sum picture and the iterated integral picture. It involves a decoration of the forests by the positive integers in the first case, by only two colours in the second case.<br />From a talk at the ESF exploratory workshop "New approaches to Multiple Zeta Values", ICMAT, Madrid, Sept-Oct. 2013
- Subjects :
- quasi-shuffle
Pure mathematics
shuffle
010103 numerical & computational mathematics
[MATH] Mathematics [math]
multiple zeta values
01 natural sciences
Surjective function
Morphism
rooted trees
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
FOS: Mathematics
Mathematics - Combinatorics
Number Theory (math.NT)
0101 mathematics
11M32
[MATH]Mathematics [math]
Mathematics
Mathematics - Number Theory
010102 general mathematics
Hopf algebra
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Formalism (philosophy of mathematics)
Iterated integrals
Iterated function
Hopf algebras
Combinatorics (math.CO)
arborification
Subjects
Details
- Language :
- English
- ISBN :
- 978-3-030-37030-5
- ISBNs :
- 9783030370305
- Database :
- OpenAIRE
- Journal :
- Periods in Quantum Field Theory and Arithmetic, Jose Ignacio Burgos Gil, Kurusch Ebrahimi-Fard, Herbert Gangl. Periods in Quantum Field Theory and Arithmetic, 314, Springer, pp.469-481, 2020, Springer Proceedings in Mathematics & Statistics book series, 978-3-030-37030-5, Springer Proceedings in Mathematics & Statistics ISBN: 9783030370305
- Accession number :
- edsair.doi.dedup.....0d48fe5145abcd4ceeb53ed6d789b8ef