Abstract
A matrix associated with the chromatic join of non-crossing partitions has been introduced by Tutte to generalise the Birkhoff-Lewis equations. A conjecture is given for its determinant in terms of polynomials having the Beraha numbers among their roots. Corresponding results for join and meet on the lattices of partitions and non-crossing partitions are 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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