ISSN:
1572-9273
Keywords:
06C05
;
05A15
;
Free modular lattices
;
partial difference equations
;
generating functions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We show that the number of elements in FM(1+1+n), the modular lattice freely generated by two single elements and an n-element chain, is 1 $$\frac{1}{{6\sqrt 2 }}\sum\limits_{k = 0}^{n + 1} {\left[ {2\left( {\begin{array}{*{20}c} {2k} \\ k \\ \end{array} } \right) - \left( {\begin{array}{*{20}c} {2k} \\ {k - 2} \\ \end{array} } \right)} \right]} \left( {\lambda _1^{n - k + 2} - \lambda _2^{n - k + 2} } \right) - 2$$ , where $$\lambda _{1,2} = {{\left( {4 \pm 3\sqrt 2 } \right)} \mathord{\left/ {\vphantom {{\left( {4 \pm 3\sqrt 2 } \right)} 2}} \right. \kern-\nulldelimiterspace} 2}$$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00346128
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