Borel orbits in the AIII and CII symmetric varieties are in bijection with matchings in (double) corona graphs, and this dictionary proves the Can-Ugurlu conjecture about non-integral orbit-counting coefficients.
Lusztig, Canonical bases arising from quantized enveloping algebra s, Journal of the Amer- ican Mathematical Society 3 (1990), no
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Matchings in Corona graph and classical symmetric varieties
Borel orbits in the AIII and CII symmetric varieties are in bijection with matchings in (double) corona graphs, and this dictionary proves the Can-Ugurlu conjecture about non-integral orbit-counting coefficients.