Latin bitrades, dissections of equilateral triangles and abelian groups

Details Latin bitrades, dissections of equilateral triangles and abelian groups Latin bitrades, dissections of equilateral triangles and abelian groups

2009-07-10

arxiv.org/abs/0907.1789v1

Mathematics

Combinatorics

Scientific paper

Let $T = (T^{\textstyle \ast}, T^{\scriptscriptstyle \triangle})$ be a spherical latin bitrade. With each $a=(a_1,a_2,a_3)\in T^{\textstyle \ast}$ associate a set of linear equations $\eq(T,a)$ of the form $b_1+b_2=b_3$, where $b = (b_1,b_2,b_3)$ runs through $T^{\textstyle \ast} \setminus \{a\}$. Assume $a_1 = 0 = a_2$ and $a_3 = 1$. Then $\eq(T,a)$ has in rational numbers a unique solution $b_i = \bar b_i$. Suppose that $\bar b_i \ne \bar c_i$ for all $b,c \in T^{\textstyle \ast}$ such that $b_i \ne c_i$ and $i \in \{1,2,3\}$. We prove that then $T^{\scriptscriptstyle \triangle}$ can be interpreted as a dissection of an equilateral triangle. We also consider group modifications of latin bitrades and show that the methods for generating the dissections can be used for a proof that $T^{\textstyle \ast}$ can be embedded into the operational table of a finite abelian group, for every spherical latin bitrade $T$.

Affiliated with

Also associated with

No associations

Rating

Latin bitrades, dissections of equilateral triangles and abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Latin bitrades, dissections of equilateral triangles and abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Latin bitrades, dissections of equilateral triangles and abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-164637