Journal of algebra, ISSN 0021-8693, 2017, Volume 481, pp. 293 - 326

Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations...

Quasi-shuffle product | Multiple zeta values | Infinitesimal Hopf algebra | Hopf algebra | MATHEMATICS | MULTIPLE HARMONIC SUMS | ZETA-STAR VALUES | Algebra

Quasi-shuffle product | Multiple zeta values | Infinitesimal Hopf algebra | Hopf algebra | MATHEMATICS | MULTIPLE HARMONIC SUMS | ZETA-STAR VALUES | Algebra

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 6/2018, Volume 22, Issue 3, pp. 529 - 543

Using the combinatorial descriptions of stuffle product, we obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values...

Multiple zeta values | Stuffle product | Multiple zeta-star values | MATHEMATICS | DECOMPOSITION | multiple zeta-star values | Stuffel product | multiple zeta values | SHUFFLE PRODUCT

Multiple zeta values | Stuffle product | Multiple zeta-star values | MATHEMATICS | DECOMPOSITION | multiple zeta-star values | Stuffel product | multiple zeta values | SHUFFLE PRODUCT

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2017, Volume 171, pp. 79 - 111

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two...

Multiple zeta values | Shuffle product | MATHEMATICS | DECOMPOSITION | SERIES | DIRICHLET FUNCTIONS

Multiple zeta values | Shuffle product | MATHEMATICS | DECOMPOSITION | SERIES | DIRICHLET FUNCTIONS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2017, Volume 233, pp. 1 - 18

We define and investigate a family of permutations matrices, called shuffling matrices, acting on a set of N=n1⋯nm elements, where m≥2 and ni≥2 for any...

Kronecker product | Shuffling matrix | Rooted tree | Perfect shuffle | Discrete Fourier Matrix | MATHEMATICS, APPLIED | CUTOFF PHENOMENON | Mathematics - Combinatorics

Kronecker product | Shuffling matrix | Rooted tree | Perfect shuffle | Discrete Fourier Matrix | MATHEMATICS, APPLIED | CUTOFF PHENOMENON | Mathematics - Combinatorics

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 5, pp. S526 - S543

The infinitesimal generator matrix underlying a multidimensional Markov chain can be represented compactly by using sums of Kronecker products of small rectangular matrices...

Markov chain | Shuffle algorithm | Vector-Kronecker product multiplication | Kronecker representation | MATHEMATICS, APPLIED | MODELS | MARKOVIAN REPRESENTATIONS | PARALLEL SYSTEMS | vector-Kronecker product multiplication | STOCHASTIC AUTOMATA NETWORKS | BLOCK SOR | MULTILEVEL METHODS | shuffle algorithm | SERVERS

Markov chain | Shuffle algorithm | Vector-Kronecker product multiplication | Kronecker representation | MATHEMATICS, APPLIED | MODELS | MARKOVIAN REPRESENTATIONS | PARALLEL SYSTEMS | vector-Kronecker product multiplication | STOCHASTIC AUTOMATA NETWORKS | BLOCK SOR | MULTILEVEL METHODS | shuffle algorithm | SERVERS

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 11/2019, Volume 42, Issue 6, pp. 3047 - 3072

.... We construct free commutative modified Rota–Baxter algebras by a variation of the shuffle product and describe the structure both recursively and explicitly...

Rota–Baxter algebra | 16S10 | Bialgebra | 16T99 | Modified Rota–Baxter algebra | Mathematics, general | Mathematics | Applications of Mathematics | Hopf algebra | Shuffle product | 16W99 | MATHEMATICS | ASSOCIATIVE ALGEBRAS | Modified Rota-Baxter algebra | Rota-Baxter algebra | O-OPERATORS | Algebra

Rota–Baxter algebra | 16S10 | Bialgebra | 16T99 | Modified Rota–Baxter algebra | Mathematics, general | Mathematics | Applications of Mathematics | Hopf algebra | Shuffle product | 16W99 | MATHEMATICS | ASSOCIATIVE ALGEBRAS | Modified Rota-Baxter algebra | Rota-Baxter algebra | O-OPERATORS | Algebra

Journal Article

Information Processing Letters, ISSN 0020-0190, 05/2019, Volume 145, pp. 68 - 73

We show that the shuffle L⊔⊔F of a piecewise-testable language L and a finite language F is piecewise-testable. The proof relies on a classic but little-used...

Piecewise-testable languages | Subwords and subsequences | Dot-depth-one and star-free languages | Shuffle product | Formal languages | COMPUTER SCIENCE, INFORMATION SYSTEMS | Computer Science - Formal Languages and Automata Theory | Computer Science

Piecewise-testable languages | Subwords and subsequences | Dot-depth-one and star-free languages | Shuffle product | Formal languages | COMPUTER SCIENCE, INFORMATION SYSTEMS | Computer Science - Formal Languages and Automata Theory | Computer Science

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2016, Volume 20, Issue 1, pp. 13 - 24

The classical Euler decomposition theorem expressed a product of two Riemann zeta values...

Integers | Mathematical theorems | Value theorems | Multiple zeta values | Shuffle product | Euler decomposition theorem | MATHEMATICS | SUM FORMULAS

Integers | Mathematical theorems | Value theorems | Multiple zeta values | Shuffle product | Euler decomposition theorem | MATHEMATICS | SUM FORMULAS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 1/2000, Volume 11, Issue 1, pp. 49 - 68

... * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be viewed as a generalization of the shuffle product III...

noncommutative symmetric function | Convex and Discrete Geometry | shuffle algebra | quantum shuffle product | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Hopf algebra | Computer Science, general | Combinatorics | quasi-symmetric function | Quantum shuffle product | Shuffle algebra | Noncommutative symmetric function | Quasi-symmetric function | MATHEMATICS | ALGEBRAS | QUANTUM GROUPS | SYMMETRICAL FUNCTIONS | Algebra

noncommutative symmetric function | Convex and Discrete Geometry | shuffle algebra | quantum shuffle product | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Hopf algebra | Computer Science, general | Combinatorics | quasi-symmetric function | Quantum shuffle product | Shuffle algebra | Noncommutative symmetric function | Quasi-symmetric function | MATHEMATICS | ALGEBRAS | QUANTUM GROUPS | SYMMETRICAL FUNCTIONS | Algebra

Journal Article

Journal of Number Theory, ISSN 0022-314X, 11/2014, Volume 144, pp. 219 - 233

In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs...

Multiple zeta values | Euler's decomposition formula | Restricted decomposition formula | Shuffle product | MIXED TATE MOTIVES | POLYLOGARITHMS | MATHEMATICS | HARMONIC SERIES | Computer science

Multiple zeta values | Euler's decomposition formula | Restricted decomposition formula | Shuffle product | MIXED TATE MOTIVES | POLYLOGARITHMS | MATHEMATICS | HARMONIC SERIES | Computer science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2013, Volume 398, Issue 1, pp. 392 - 402

.... in terms of MCD copulas and the ∗-product discovered by Darsow, Nguyen and Olsen. Since any shuffle of a copula is the copula of the corresponding shuffle of the two...

Shuffles of copulas | Shuffles of Min | Measure-preserving | Copulas | Sobolev norm [formula omitted]-product | Measure of dependence | Sobolev norm -product | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT

Shuffles of copulas | Shuffles of Min | Measure-preserving | Copulas | Sobolev norm [formula omitted]-product | Measure of dependence | Sobolev norm -product | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT

Journal Article

Kybernetika, ISSN 0023-5954, 2007, Volume 43, Issue 2, pp. 235 - 244

.... In particular, these constructions are generalizations of the *-product and the *-product for copulas introduced by Darsow, Nguyen and Olsen in 1992...

Ordinal sum | Shuffle of Min | Copula | Concordance | shuffle of Min | copula | ordinal sum | COMPUTER SCIENCE, CYBERNETICS | concordance

Ordinal sum | Shuffle of Min | Copula | Concordance | shuffle of Min | copula | ordinal sum | COMPUTER SCIENCE, CYBERNETICS | concordance

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2017

.... A word u∈A* is a square for the shuffle product if it is the shuffle of two identical words (i.e., u∈v[U+29E2]v for some v...

Combinatorics on words | Complexity | Shuffle operator | Data Structures and Algorithms | Computer Science

Combinatorics on words | Complexity | Shuffle operator | Data Structures and Algorithms | Computer Science

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 06/2020, Volume 224, Issue 6, p. 106260

For a prime number p and a free profinite group S on the basis X, let S(n,p), n=1,2,…, be the lower p-central filtration of S. For p>n, we give a combinatorial...

Massey products | Lower p-central sequence | Absolute Galois groups | Shuffle algebra | Unipotent upper-triangular representations | Galois cohomology | MATHEMATICS | MATHEMATICS, APPLIED | QUOTIENTS | representations | TRIPLE MASSEY PRODUCTS | Unipotent upper-triangular

Massey products | Lower p-central sequence | Absolute Galois groups | Shuffle algebra | Unipotent upper-triangular representations | Galois cohomology | MATHEMATICS | MATHEMATICS, APPLIED | QUOTIENTS | representations | TRIPLE MASSEY PRODUCTS | Unipotent upper-triangular

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 2005, Volume 200, Issue 3, pp. 293 - 317

.... We consider these constructions as operads and their products and duals, in terms of generators and relations, with the goal to clarify and simplify the process of obtaining new algebra structures...

SHUFFLE PRODUCTS | MATHEMATICS | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | TREES | THEOREM | QUANTUM-FIELD THEORY | BAXTER ALGEBRAS | HOMOLOGY | RENORMALIZATION | DIALGEBRAS

SHUFFLE PRODUCTS | MATHEMATICS | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | TREES | THEOREM | QUANTUM-FIELD THEORY | BAXTER ALGEBRAS | HOMOLOGY | RENORMALIZATION | DIALGEBRAS

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 08/2014, Volume 13, Issue 5, pp. 1350160 - 1-1350160-38

In this paper, we construct free commutative integro-differential algebras by applying the method of Grobner-Shirshov bases. We establish the...

Differential algebra | Free algebra | Rota-Baxter algebra | Gröbner-Shirshov basis | Shuffle product | Integro-differential algebra | Mixable shuffle product | MATHEMATICS, APPLIED | shuffle product | Grobner-Shirshov basis | integro-differential algebra | SHUFFLE PRODUCTS | MATHEMATICS | free algebra | COMBINATORIAL IDENTITIES | ROTA-BAXTER ALGEBRAS | DIAMOND LEMMA | mixable shuffle product | Construction | Algebra

Differential algebra | Free algebra | Rota-Baxter algebra | Gröbner-Shirshov basis | Shuffle product | Integro-differential algebra | Mixable shuffle product | MATHEMATICS, APPLIED | shuffle product | Grobner-Shirshov basis | integro-differential algebra | SHUFFLE PRODUCTS | MATHEMATICS | free algebra | COMBINATORIAL IDENTITIES | ROTA-BAXTER ALGEBRAS | DIAMOND LEMMA | mixable shuffle product | Construction | Algebra

Journal Article

Ramanujan Journal, ISSN 1382-4090, 2019, Volume 49, Issue 1, pp. 215 - 230

In this paper we give two idelic representations of the multiple zeta valuesone using iterated integrals over the finite ideles and the other using iterated...

Multiple zeta values | Adeles | Shuffle product | Iterated integrals | MATHEMATICS | Computer science | Community colleges

Multiple zeta values | Adeles | Shuffle product | Iterated integrals | MATHEMATICS | Computer science | Community colleges

Journal Article

International Journal of Algebra and Computation, ISSN 0218-1967, 06/2017, Volume 27, Issue 4, pp. 421 - 454

... of the Künneth formula for direct products; and plactic monoids. Our key result is an identification of the (co...

cup product | monoid factorization | quadratic normalization | shuffle (co)product | Steenrod operations | Hochschild (co)homology | structure monoid | idempotent braiding | Yang-Baxter equation | Coxeter monoid | braided (co)homology | 0 -Hecke monoid | quantum symmetrizer | 0-Hecke monoid | OPERATIONS | I-TYPE | GRAPHS | SET-THEORETICAL SOLUTIONS | MATHEMATICS | RACK | COXETER MONOIDS | ALGEBRAS | QUANTUM SHUFFLES | HOMOLOGY | Web services

cup product | monoid factorization | quadratic normalization | shuffle (co)product | Steenrod operations | Hochschild (co)homology | structure monoid | idempotent braiding | Yang-Baxter equation | Coxeter monoid | braided (co)homology | 0 -Hecke monoid | quantum symmetrizer | 0-Hecke monoid | OPERATIONS | I-TYPE | GRAPHS | SET-THEORETICAL SOLUTIONS | MATHEMATICS | RACK | COXETER MONOIDS | ALGEBRAS | QUANTUM SHUFFLES | HOMOLOGY | Web services

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2017, Volume 489, pp. 552 - 581

An internal coproduct is described, which is compatible with Hoffman's quasi-shuffle product...

B- and S-series | Surjections | Bialgebra | Weak quasi-shuffle | Word series | Rooted trees | Arborification | Comodule-Hopf algebra | Quasi-shuffle product | Mould calculus | Hopf algebra | HOPF-ALGEBRAS | LIE ENVELOPING ALGEBRA | MATHEMATICS | PRODUCTS | Algebra

B- and S-series | Surjections | Bialgebra | Weak quasi-shuffle | Word series | Rooted trees | Arborification | Comodule-Hopf algebra | Quasi-shuffle product | Mould calculus | Hopf algebra | HOPF-ALGEBRAS | LIE ENVELOPING ALGEBRA | MATHEMATICS | PRODUCTS | Algebra

Journal Article

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

.... Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.

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

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

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.