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On the Quiver Presentation of the Descent Algebra of the Symmetric Group
Descent algebra symmetric group quiver presentation
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...
The universal Askey-Wilson algebra and the equitable presentation of $U_q(\mathfrak{sl}_2)$
Askey-Wilson relations Leonard pair Casimir element
2011/9/14
Abstract: Let $F$ denote a field, and fix a nonzero $q \in F$ such that $q^4\not=1$. The universal Askey-Wilson algebra is the associative $F$-algebra $\Delta=\Delta_q$ defined by generators and relat...
An Alternative Presentation of the Symmetric-Simplicial Category
Alternative Presentation Symmetric-Simplicial Category
2011/1/19
t0, 1, . . . nuto include all functions between the same sets. Marco Grandis [Gra01a] has given a presentation of Fin using the standard generators di and si of Ord as well as the adjacent transpositi...
A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties
conjugation-free geometric presentation of fundamental groups some properties
2010/12/1
A conjugation-free geometric presentation of a funda-mental group is a presentation with the natural topological gener-ators x1, . . . , xn and the cyclic relations.
Visually Dynamic Presentation of Proofs in Plane Geometry Part 1. Basic Features and the Manual Input Method
Geometry theorem proving Visually dynamic presentation of proof Dynamic geometry Unordered geometry Gelernter Java Geometry Expert Morley’s theorem Feuerbach’s theorem Pythagorean theorem Pedal triangle
2013/9/9
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...
Visually Dynamic Presentation of Proofs in Plane Geometry
Geometry theorem proving Proof with hierarchical structures Visually dynamic presentation of proof Dynamic geometry Full-angle Deductive database Fixpoint Unordered geometry Hilbert geometry Tarski geometry
2013/9/9
We present the method for automated generation of visually dynamic presentations of plane geometry proofs based on the full-angle method. The proof generated by the full-angle method is organized hier...