Antiassociative groupoids

Braitt, Milton, Hobby, David, and Silberger, Donald. "Antiassociative groupoids." Mathematica Bohemica 142.1 (2017): 27-46. <http://eudml.org/doc/287871>.

@article{Braitt2017,
abstract = {Given a groupoid $\langle G, \star \rangle $, and $k \ge 3$, we say that $G$ is antiassociative if an only if for all $x_1, x_2, x_3 \in G$, $(x_1 \star x_2) \star x_3$ and $x_1 \star (x_2 \star x_3)$ are never equal. Generalizing this, $\langle G, \star \rangle $ is $k$-antiassociative if and only if for all $x_1, x_2, \ldots , x_k \in G$, any two distinct expressions made by putting parentheses in $x_1 \star x_2 \star x_3 \star \cdots \star x_k$ are never equal. We prove that for every $k \ge 3$, there exist finite groupoids that are $k$-antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.},
author = {Braitt, Milton, Hobby, David, Silberger, Donald},
journal = {Mathematica Bohemica},
keywords = {groupoid; unification; dissociative groupoids; generalized associative groupoids; formal products; reverse Polish notation},
language = {eng},
number = {1},
pages = {27-46},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Antiassociative groupoids},
url = {http://eudml.org/doc/287871},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Braitt, Milton
AU - Hobby, David
AU - Silberger, Donald
TI - Antiassociative groupoids
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 1
SP - 27
EP - 46
AB - Given a groupoid $\langle G, \star \rangle $, and $k \ge 3$, we say that $G$ is antiassociative if an only if for all $x_1, x_2, x_3 \in G$, $(x_1 \star x_2) \star x_3$ and $x_1 \star (x_2 \star x_3)$ are never equal. Generalizing this, $\langle G, \star \rangle $ is $k$-antiassociative if and only if for all $x_1, x_2, \ldots , x_k \in G$, any two distinct expressions made by putting parentheses in $x_1 \star x_2 \star x_3 \star \cdots \star x_k$ are never equal. We prove that for every $k \ge 3$, there exist finite groupoids that are $k$-antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.
LA - eng
KW - groupoid; unification; dissociative groupoids; generalized associative groupoids; formal products; reverse Polish notation
UR - http://eudml.org/doc/287871
ER -