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When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

The

**free**product G*H of groups G and H is the set of elements of the form g_1h_1g_2h_2...g_rh_r, where g_i in G and h_i in H, with g_1 and h_r possibly equal to e, the ...A group action G×X->X is called

**free**if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is**free**if the map G×X->X×X ...A group is called a

**free**group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...A

**free**Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...A tree which is not rooted, i.e., a normal tree with no node singled out for special treatment (Skiena 1990, p. 107).

**Free**trees are sometimes known instead as unrooted trees ...A

**free**idempotent monoid is a monoid that satisfies the identity x^2=x and is generated by a set of elements. If the generating set of such a monoid is finite, then so is the ...A triangle-

**free**graph is a graph containing no graph cycles of length three. A simple graph is triangle-**free**iff Tr(A^3)=0, where A is the adjacency matrix of the graph and ...A RAT-

**free**("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-**free**subset of ...A sum-

**free**set S is a set for which the intersection of S and the sumset S+S is empty. For example, the sum-**free**sets of {1,2,3} are emptyset, {1}, {2}, {3}, {1,3}, and ......