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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Equivalent pairs of words and points of connection
1Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan.
Abstract:
Higman has defined coset diagrams for PGL(2, ℤ). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in ℤ[𝔃], obtained by choosing a pair of words F[w i , w j ] such that both w i and w j fix a vertex v in γ. Two pairs of words are equivalent if and only if they have the same polynomial. In this paper, we find distinct pairs of words that are equivalent. We also show there are certain fragments, which have the same orientations as those of their mirror images.
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