What is freely reduced?

Some articles on freely reduced, reduced:

Van Kampen Diagram - Van Kampen Lemma
... (†) with boundary label w which is a word (not necessarily freely reduced) in the alphabet A ∪ A−1 ... Let w be a freely reduced word in the alphabet A ∪ A−1 such that w=1 in G ... Then there exists a reduced van Kampen diagram over the presentation (†) whose boundary label is freely reduced and is equal to w ...
Van Kampen Diagram - Van Kampen Lemma - Sketch of The Proof
... First, it is easy to see that if w is freely reduced and w = 1 in G there exists some van Kampen diagram with boundary label w0 such that w = w0 in F(A) (after ... However, it is possible that the word w0 is not freely reduced ... to get a sequence of van Kampen diagrams by making their boundary labels more and more freely reduced and making sure that at each step the boundary label of each diagram in the sequence is ...
Van Kampen Diagram
... of the boundary cycle of the region read from that vertex and in that direction is a freely reduced word in F(A) that belongs to R∗ ... label of the region read from that vertex and in that direction is freely reduced and belongs to R ... alphabet A ∪ A−1 (which is not necessarily freely reduced) that is called the boundary label of ...

Famous quotes containing the words reduced and/or freely:

    Narrowed-down by her early editors and anthologists, reduced to quaintness or spinsterish oddity by many of her commentators, sentimentalized, fallen-in-love with like some gnomic Garbo, still unread in the breadth and depth of her full range of work, she was, and is, a wonder to me when I try to imagine myself into that mind.
    Adrienne Rich (b. 1929)

    Why the jailer does not leave open his prison doors,—why the judge does not dismiss his case,—why the preacher does not dismiss his congregation! It is because they do not obey the hint God gives them, nor accept the pardon which he freely offers to all.
    Henry David Thoreau (1817–1862)