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.
The genesis of involutions (polarizations and lattice paths)
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
The number of Borel orbits in polarizations (the symmetric variety $SL(n)/S(GL(p)\times GL(q))$) is analyzed, various (bivariate) generating functions are found. Relations to lattice path combinatorics are explored.
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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.