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Abstract
We study the Poincare polynomials of all known Calabi-Yau three-folds as constrained
polynomials of Littlewood type, thus generalising the well-known investigation into
the distribution of the Euler characteristic and Hodge numbers. We find interesting
fractal behaviour in the roots of these polynomials in relation to the existence of
isometries, distribution versus typicality, and mirror symmetry.
Comments 14 pages, 6 figures, invited contribution to the Max Kreuzer Memorial
Volume, based on MPhys project of the first author under the supervision of
the second, at the University of Oxford