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Combinatorics of the free Baxter algebra
free Baxter algebra Combinatorics
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2015/8/14
We study the free (associative, non-commutative) Baxter algebra on one generator.
The first explicit description of this object is due to Ebrahimi-Fard and
Guo. We provide an alternative description...
THE PEAK ALGEBRA AND THE DESCENT ALGEBRAS OF TYPES B AND D
peak algebra signed permutations Coxeter groups
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2015/8/14
We show the existence of a unital subalgebra Pn of the symmetric group
algebra linearly spanned by sums of permutations with a common peak set, which we
call the peak algebra. We show that Pn is the...
THE HOPF ALGEBRA OF UNIFORM BLOCK PERMUTATIONS
Hopf algebra factorizable inverse monoid uniform block permutation
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2015/8/14
We introduce the Hopf algebra of uniform block permutations and show that
it is self-dual, free, and cofree. These results are closely related to the fact that uniform
block permutations form a fact...
A GROWTH MODEL,A GAME,AN ALGEBRA,LAGRANGE INVERSION,AND CHARACTERISTIC CLASSES
Growth model games algebra Lagrange inversion feature classes
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2015/7/14
A GROWTH MODEL,A GAME,AN ALGEBRA,LAGRANGE INVERSION,AND CHARACTERISTIC CLASSES.
Analysis of Systematic Scan Metropolis Algorithms Using Iwahori–Hecke Algebra Techniques
Analysis system scanning the metropolis algorithm Iwahori - Hecke algebraic techniques
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2015/7/14
Analysis of Systematic Scan Metropolis Algorithms Using Iwahori–Hecke Algebra Techniques。
SUPERCHARACTERS AND SUPERCLASSES FOR ALGEBRA GROUPS
SUPERCHARACTERS super class of algebraic groups
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2015/7/8
SUPERCHARACTERS AND SUPERCLASSES FOR ALGEBRA GROUPS。
On Hopf algebra structures over operads
Hopf algebra operads
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2015/3/25
We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the noncommutative plan...
Operads, homotopy algebra and iterated integrals for double loop spaces
Operads homotopy algebra iterated integrals double loop spaces
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2015/3/25
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
On Spineless Cacti, Deligne's Conjecture and Connes--Kreimer's Hopf Algebra
Spineless Cacti Deligne's Conjecture Connes--Kreimer's Hopf Algebra
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2015/3/25
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to ...
Learning to Automatically Solve Algebra Word Problems
Algebra Word Problems Automatically
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2014/11/26
Learning to Automatically Solve Algebra Word Problems。
Representations of the Kauffman skein algebra II: punctured surfaces
Representations of the Kauffman skein algebra II punctured surfaces Geometric Topology
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2012/6/29
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants a...
Representations of the Kauffman skein algebra I: invariants and miraculous cancellations
Representations of the Kauffman skein algebra I invariants miraculous cancellations Geometric Topology
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2012/6/29
We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is ...
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis
Derivations and Projections Jordan Triples nonassociative algebra continuous cohomology quantum functional analysis Operator Algebras
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2012/6/19
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
Markov trace on Funar algebra
Markov trace Funar algebra Geometric Topology
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2012/6/21
Funar algebra $K_\infty=K_\infty(\alpha,\beta;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $\sigma_1^3-\alpha\sigma_1^2+\beta\sigma_1-...
On the Quiver Presentation of the Descent Algebra of the Symmetric Group
Descent algebra symmetric group quiver presentation
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2012/6/15
We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic...