895 research outputs found
Exponential series without denominators
For a commutative algebra which comes from a Zinbiel algebra the exponential
series can be written without denominators. When lifted to dendriform algebras
this new series satisfies a functional equation analogous to the
Baker-Campbell-Hausdorff formula. We make it explicit by showing that the
obstruction series is the sum of the brace products. In the multilinear case we
show that the role the Eulerian idempotent is played by the iterated pre-Lie
product.Comment: 13
The YY game
We introduce a new one-person game similar to the Sudoku game. It is based on
combinatorial objects called planar binary rooted trees. It is related to the
four color conjecture. Its mathematical analysis makes use of the Tamari poset,
hence the Stasheff associahedron.Comment: 7 page
On Products and Duality of Binary, Quadratic, Regular Operads
Since its introduction by Loday in 1995 with motivation from algebraic
K-theory, dendriform dialgebras have been studied quite extensively with
connections to several areas in mathematics and physics. A few more similar
structures have been found recently, such as the tri-, quadri-, ennea- and
octo-algebras, with increasing complexity in their constructions and
properties. 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 from known structures
and from linear operators.Comment: 22 page
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