Periodic scale: Difference between revisions
Wikispaces>genewardsmith **Imported revision 401004470 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 401004574 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-24 04: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-24 04:28:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>401004574</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The set {s[i]|i∈ℤ} generates a group G, the **group of the scale**; this is a free, finitely generated subgroup of the reals ℝ. | The set {s[i]|i∈ℤ} generates a group G, the **group of the scale**; this is a free, finitely generated subgroup of the reals ℝ. | ||
**Epimorphic**: If there exists a homomorphism h:G⟶ℤ for which s is a transversal, so that h(s[i]) = i, then s is weakly epimorphic with the homomorphism h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were apparently first considered by [[Yves Hellegouarch]] | **Epimorphic**: If there exists a homomorphism h:G⟶ℤ for which s is a transversal, so that h(s[i]) = i, then s is weakly epimorphic with the homomorphism h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were apparently first considered by [[Yves Hellegouarch]]. | ||
**[[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]]** : A monotone scale in which every class but classes nP have exactly two elements has Myhill's property. If every such class has exactly three elements, it has the **trivalence property**. If every class has less than three elements, it has the property of distributional evenness.</pre></div> | **[[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]]** : A monotone scale in which every class but classes nP have exactly two elements has Myhill's property. If every such class has exactly three elements, it has the **trivalence property**. If every class has less than three elements, it has the property of distributional evenness.</pre></div> | ||
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The set {s[i]|i∈ℤ} generates a group G, the <strong>group of the scale</strong>; this is a free, finitely generated subgroup of the reals ℝ.<br /> | The set {s[i]|i∈ℤ} generates a group G, the <strong>group of the scale</strong>; this is a free, finitely generated subgroup of the reals ℝ.<br /> | ||
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<strong>Epimorphic</strong>: If there exists a homomorphism h:G⟶ℤ for which s is a transversal, so that h(s[i]) = i, then s is weakly epimorphic with the homomorphism h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were apparently first considered by <a class="wiki_link" href="/Yves%20Hellegouarch">Yves Hellegouarch</a> | <strong>Epimorphic</strong>: If there exists a homomorphism h:G⟶ℤ for which s is a transversal, so that h(s[i]) = i, then s is weakly epimorphic with the homomorphism h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were apparently first considered by <a class="wiki_link" href="/Yves%20Hellegouarch">Yves Hellegouarch</a>.<br /> | ||
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<strong><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's property</a></strong> : A monotone scale in which every class but classes nP have exactly two elements has Myhill's property. If every such class has exactly three elements, it has the <strong>trivalence property</strong>. If every class has less than three elements, it has the property of distributional evenness.</body></html></pre></div> | <strong><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's property</a></strong> : A monotone scale in which every class but classes nP have exactly two elements has Myhill's property. If every such class has exactly three elements, it has the <strong>trivalence property</strong>. If every class has less than three elements, it has the property of distributional evenness.</body></html></pre></div> | ||