Rank-3 scale theorems
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- This revision was by author mbattaglia1 and made on 2011-11-14 13:04:05 UTC.
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=Theorems= * Every triple Fokker block is max variety 3. * Every max variety 3 block is a triple Fokker block. * Triple Fokker blocks form a trihexagonal tiling on the lattice. * Every Fokker block is the product word of two MOS scales. See <span style="background-color: #ffffff; color: #1155cc; font-family: arial,sans-serif;">[[@http://www.springerlink.com/content/c23748337406x463/]]</span> * If the step sizes for a rank-3 Fokker block are L, m, n, and s, where L > m > n > s, then the following identity must hold: (n-s) + (m-s) = (L-s), hence n+m=L+s =Unproven Conjectures= * Every rank-3 Fokker block has mean-variety < 4, meaning that some interval class will come in less than 4 sizes.
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<html><head><title>Rank-3 scale theorems</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Theorems"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theorems</h1> <ul><li>Every triple Fokker block is max variety 3.</li><li>Every max variety 3 block is a triple Fokker block.</li><li>Triple Fokker blocks form a trihexagonal tiling on the lattice.</li><li>Every Fokker block is the product word of two MOS scales. See <span style="background-color: #ffffff; color: #1155cc; font-family: arial,sans-serif;"><a class="wiki_link_ext" href="http://www.springerlink.com/content/c23748337406x463/" rel="nofollow" target="_blank">http://www.springerlink.com/content/c23748337406x463/</a></span></li><li>If the step sizes for a rank-3 Fokker block are L, m, n, and s, where L > m > n > s, then the following identity must hold: (n-s) + (m-s) = (L-s), hence n+m=L+s</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Unproven Conjectures"></a><!-- ws:end:WikiTextHeadingRule:2 -->Unproven Conjectures</h1> <ul><li>Every rank-3 Fokker block has mean-variety < 4, meaning that some interval class will come in less than 4 sizes.</li></ul></body></html>