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The Lattice of Non-crossing Partitions and the Birkhoff-Lewis Equations

✍ Scribed by D.M. Jackson

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
186 KB
Volume
15
Category
Article
ISSN
0195-6698

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✦ Synopsis

A matrix associated with the chromatic join of non-crossing partitions has been introduced by Tutte to generalise the Birkhoff-Lewis equations. A conjecturc is given for its determinant in terms of polynomials having the Beraha numbers among their roots. Corrcsponding results for join and meet on the lattices of partitions and non-crossing partitions arc obtained in terms of the combinatorial invariants of the lattices. The conjecture is restated in terms the lattice of non-crossing partitions alone.

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