Journal of Algebra, ISSN 0021-8693, 02/2020, Volume 543, pp. 111 - 155

....•An explicit relation between AZVs and Multi Zeta Values (MZVs).•New (to my knowledge) proofs of some of the properties of the MZVs, proofs obtained by purely algebraic means...

Multiple zeta values | Rooted trees | Shuffle products | Rota-Baxter algebras | MATHEMATICS

Multiple zeta values | Rooted trees | Shuffle products | Rota-Baxter algebras | MATHEMATICS

Journal Article

ACM Transactions on Computational Logic (TOCL), ISSN 1529-3785, 06/2017, Volume 18, Issue 2, pp. 1 - 41

...: they need comparing labels of paths based on word relations (such as prefix, subword, or subsequence...

Complexity of evaluation | regular path queries | rational relations | logics for graphs | shuffle | word equations | Logics for graphs | Regular path queries | Shuffle | Word equations | Rational relations | Theory | EQUATIONS | Languages | LOGIC | Algorithms | QUERY LANGUAGES | COMPUTER SCIENCE, THEORY & METHODS

Complexity of evaluation | regular path queries | rational relations | logics for graphs | shuffle | word equations | Logics for graphs | Regular path queries | Shuffle | Word equations | Rational relations | Theory | EQUATIONS | Languages | LOGIC | Algorithms | QUERY LANGUAGES | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Compositio mathematica, ISSN 0010-437X, 3/2006, Volume 142, Issue 2, pp. 307 - 338

Derivation and extended double shuffle (EDS) relations for multiple zeta values (MZVs) are proved. Related algebraic structures of MZVs, as well...

Derivation | Double shuffle relation | Multiple zeta value | Regularization | MATHEMATICS | HARMONIC SERIES | ALGEBRA | regularization | multiple zeta value | derivation | double shuffle relation

Derivation | Double shuffle relation | Multiple zeta value | Regularization | MATHEMATICS | HARMONIC SERIES | ALGEBRA | regularization | multiple zeta value | derivation | double shuffle relation

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 10/2017, Volume 13, Issue 9, pp. 2245 - 2251

.... We call these t -MZVs. In this paper, we establish the shuffle product for t -MZVs to prove Hoffman type relation and double shuffle relation for t -MZVs.

MATHEMATICS | double shuffle structure | Hoffman's relation | Interpolated multiple zeta values | HARMONIC SERIES | STAR VALUES

MATHEMATICS | double shuffle structure | Hoffman's relation | Interpolated multiple zeta values | HARMONIC SERIES | STAR VALUES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2014, Volume 252, pp. 343 - 381

.... The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values...

Conical zeta values | Convex cones | Smooth cones | Quasi-shuffles | Subdivisions | Fractions with linear poles | Decorated cones | Shuffles | Multiple zeta values | Shintani zeta values | EULER-MACLAURIN FORMULA | MULTIPLE HARMONIC SERIES | DOUBLE SHUFFLE RELATIONS | POLYTOPES | MIXED TATE MOTIVES | MATHEMATICS | RENORMALIZATION | Computer science

Conical zeta values | Convex cones | Smooth cones | Quasi-shuffles | Subdivisions | Fractions with linear poles | Decorated cones | Shuffles | Multiple zeta values | Shintani zeta values | EULER-MACLAURIN FORMULA | MULTIPLE HARMONIC SERIES | DOUBLE SHUFFLE RELATIONS | POLYTOPES | MIXED TATE MOTIVES | MATHEMATICS | RENORMALIZATION | Computer science

Journal Article

6.
Full Text
Explicit double shuffle relations and a generalization of Eulerʼs decomposition formula

Journal of Algebra, ISSN 0021-8693, 04/2013, Volume 380, pp. 46 - 77

We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms...

Multiple zeta values | Double shuffle relation | Eulerʼs decomposition formula | Multiple polylogarithm values | Euler's decomposition formula | MATHEMATICS | MULTIPLE ZETA-VALUES | ALGEBRAS | FEYNMAN DIAGRAMS | MOTIVES | RENORMALIZATION

Multiple zeta values | Double shuffle relation | Eulerʼs decomposition formula | Multiple polylogarithm values | Euler's decomposition formula | MATHEMATICS | MULTIPLE ZETA-VALUES | ALGEBRAS | FEYNMAN DIAGRAMS | MOTIVES | RENORMALIZATION

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 298, pp. 254 - 285

... both shuffle as well as quasi-shuffle relations. The corresponding products are related in terms of duality...

Rota–Baxter algebra | Double shuffle relations | Hoffman–Ohno relation | Infinitesimal bialgebra | q-Analogues | Derivation relations | Multiple zeta values | Duality | Hopf algebra | Hoffman-Ohno relation | Rota-Baxter algebra | Q-Analogues | MATHEMATICS | Algebra | Singers | Mathematics - Number Theory

Rota–Baxter algebra | Double shuffle relations | Hoffman–Ohno relation | Infinitesimal bialgebra | q-Analogues | Derivation relations | Multiple zeta values | Duality | Hopf algebra | Hoffman-Ohno relation | Rota-Baxter algebra | Q-Analogues | MATHEMATICS | Algebra | Singers | Mathematics - Number Theory

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2013, Volume 133, Issue 2, pp. 596 - 610

We prove that the Ohno–Zagier relation of multiple zeta values can be deduced from the regularized double shuffle relation...

Regularized double shuffle relation | Multiple zeta value | Ohno–Zagier relation | Ohno-Zagier relation | MATHEMATICS | SERIES

Regularized double shuffle relation | Multiple zeta value | Ohno–Zagier relation | Ohno-Zagier relation | MATHEMATICS | SERIES

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2015, Volume 17, Issue 10, pp. 2643 - 2671

We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system...

Nichols algebras | Pointed Hopf algebras | Quantized enveloping algebras | MATHEMATICS, APPLIED | PBW-BASES | RIGHT COIDEAL SUBALGEBRAS | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | THEOREM | CLASSIFICATION | MATHEMATICS | pointed Hopf algebras | SHUFFLES | MATRICES | quantized enveloping algebras

Nichols algebras | Pointed Hopf algebras | Quantized enveloping algebras | MATHEMATICS, APPLIED | PBW-BASES | RIGHT COIDEAL SUBALGEBRAS | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | THEOREM | CLASSIFICATION | MATHEMATICS | pointed Hopf algebras | SHUFFLES | MATRICES | quantized enveloping algebras

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 8/2011, Volume 25, Issue 3, pp. 307 - 317

Partial fraction methods play an important role in the study of multiple zeta values. One class of such fractions is related to the integral representations of...

Fourier Analysis | 11M41 | 11M99 | Functions of a Complex Variable | Partial fraction | Shuffles | Field Theory and Polynomials | Multiple zeta values | 40B05 | Mathematics | Number Theory | Combinatorics | MATHEMATICS | MOTIVES | Computer science

Fourier Analysis | 11M41 | 11M99 | Functions of a Complex Variable | Partial fraction | Shuffles | Field Theory and Polynomials | Multiple zeta values | 40B05 | Mathematics | Number Theory | Combinatorics | MATHEMATICS | MOTIVES | Computer science

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 06/2004, Volume 11, Issue 1

We give the construction of a free commutative unital associative Nijenhuis algebra on a commutative unital associative algebra based on an augmented modified...

MATHEMATICS | MATHEMATICS, APPLIED | modified quasi-shuffle | quasi-shuffle | Rota-Baxter relation | Loday-type algebras | BAXTER ALGEBRAS | associative Nijenhuis relation

MATHEMATICS | MATHEMATICS, APPLIED | modified quasi-shuffle | quasi-shuffle | Rota-Baxter relation | Loday-type algebras | BAXTER ALGEBRAS | associative Nijenhuis relation

Journal Article

International Journal of Information Security, ISSN 1615-5262, 2/2011, Volume 10, Issue 1, pp. 49 - 60

.... A relation attack is a serious threat to privacy of any mix network and can attack various mix networks in many ways...

Generality | Data Encryption | Novel countermeasure | Management of Computing and Information Systems | Mix network | Operating Systems | High efficiency | Computer Science | E-voting | Communications Engineering, Networks | Coding and Information Theory | Computer Communication Networks | Relation attack | COMPUTER SCIENCE, INFORMATION SYSTEMS | SHUFFLE | FLAWS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SECURE | COMPUTER SCIENCE, THEORY & METHODS | NET | Algorithms | Studies | Network security | Online voting | Networks | Voting | Countermeasures | Military technology | Computer information security | Channels

Generality | Data Encryption | Novel countermeasure | Management of Computing and Information Systems | Mix network | Operating Systems | High efficiency | Computer Science | E-voting | Communications Engineering, Networks | Coding and Information Theory | Computer Communication Networks | Relation attack | COMPUTER SCIENCE, INFORMATION SYSTEMS | SHUFFLE | FLAWS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SECURE | COMPUTER SCIENCE, THEORY & METHODS | NET | Algorithms | Studies | Network security | Online voting | Networks | Voting | Countermeasures | Military technology | Computer information security | Channels

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 1/2014, Volume 33, Issue 1, pp. 1 - 21

.... The proof uses a theorem of Imamoḡlu and Kohnen, and the double shuffle relations satisfied by the double Eisenstein series of level 2.

Double shuffle relations | Fourier Analysis | Functions of a Complex Variable | 11M32 | Double Eisenstein series | Field Theory and Polynomials | 11D85 | Eisenstein series | Mathematics | Number Theory | Sums of squares | Combinatorics | MATHEMATICS | JACOBI ELLIPTIC FUNCTIONS | INFINITE FAMILIES | FORMULAS

Double shuffle relations | Fourier Analysis | Functions of a Complex Variable | 11M32 | Double Eisenstein series | Field Theory and Polynomials | 11D85 | Eisenstein series | Mathematics | Number Theory | Sums of squares | Combinatorics | MATHEMATICS | JACOBI ELLIPTIC FUNCTIONS | INFINITE FAMILIES | FORMULAS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 11/2008, Volume 91, Issue 5, pp. 409 - 415

In this short note we will provide a new proof of the following exotic shuffle relation of multiple zeta values...

shuffle relations | WZ method | Multiple zeta values | Mathematics, general | Mathematics | Secondary 11Y99 | Primary 05A19, 11M99, 68R15 | Shuffle relations | MATHEMATICS | Algorithms

shuffle relations | WZ method | Multiple zeta values | Mathematics, general | Mathematics | Secondary 11Y99 | Primary 05A19, 11M99, 68R15 | Shuffle relations | MATHEMATICS | Algorithms

Journal Article

15.
Full Text
Iterated integrals on P 1 ∖{0,1,∞,z} and a class of relations among multiple zeta values

Advances in Mathematics, ISSN 0001-8708, 05/2019, Volume 348, pp. 163 - 182

In this paper we consider iterated integrals on P ∖{0,1,∞,z} and define a class of Q-linear relations among them, which arises from the differential structure of the iterated integrals with respect to z...

Regularized double shuffle relation | Double shuffle relation | Multiple zeta values | Hyperlogarithms | Duality relation | Iterated integrals | MATHEMATICS

Regularized double shuffle relation | Double shuffle relation | Multiple zeta values | Hyperlogarithms | Duality relation | Iterated integrals | MATHEMATICS

Journal Article

Fundamenta Informaticae, ISSN 0169-2968, 03/2004, Volume 59, Issue 4, pp. 349 - 363

.... We give general characterizations of reflexivity, transitivity, anti-symmetry and other properties of binary relations, and investigate the associated decision problems...

Shuffle on trajectories | Embedding order | Convexity | embedding order | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SHUFFLE | shuffle on trajectories | convexity | CONTEXT-FREE LANGUAGES

Shuffle on trajectories | Embedding order | Convexity | embedding order | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SHUFFLE | shuffle on trajectories | convexity | CONTEXT-FREE LANGUAGES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2016, Volume 106, Issue 9, pp. 1265 - 1316

...(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday–Gaiotto–Tachikawa relations...

Geometry | Ext operators | 81T13 | 81R10 | Theoretical, Mathematical and Computational Physics | Nekrasov partition function | shuffle algebra | AGT relations | Group Theory and Generalizations | 14D21 | Statistical Physics, Dynamical Systems and Complexity | Physics | A | PHYSICS, MATHEMATICAL | MODULI | Algebra

Geometry | Ext operators | 81T13 | 81R10 | Theoretical, Mathematical and Computational Physics | Nekrasov partition function | shuffle algebra | AGT relations | Group Theory and Generalizations | 14D21 | Statistical Physics, Dynamical Systems and Complexity | Physics | A | PHYSICS, MATHEMATICAL | MODULI | Algebra

Journal Article

18.
Full Text
Iterated integrals on P1∖{0,1,∞,z} and a class of relations among multiple zeta values

Advances in Mathematics, ISSN 0001-8708, 05/2019, Volume 348, pp. 163 - 182

In this paper we consider iterated integrals on P1∖{0,1,∞,z} and define a class of Q-linear relations among them, which arises from the differential structure of the iterated integrals with respect to z...

Regularized double shuffle relation | Multiple zeta values | Double shuffle relation | Hyperlogarithms | Duality relation | Iterated integrals

Regularized double shuffle relation | Multiple zeta values | Double shuffle relation | Hyperlogarithms | Duality relation | Iterated integrals

Journal Article

Journal of number theory, ISSN 0022-314X, 06/2019

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2020, Volume 556, pp. 363 - 384

In this paper, we prove certain algebraic identities, which correspond to differentiation of the shuffle relation, the stuffle relation, and the relations which arise...

Multiple zeta values | Shuffle product | Stuffle product | Linear fractional transformation | Iterated integrals | MATHEMATICS

Multiple zeta values | Shuffle product | Stuffle product | Linear fractional transformation | Iterated integrals | MATHEMATICS

Journal Article

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