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The genesis of involutions (polarizations and lattice paths)

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arxiv 1703.09881 v2 pith:PHB6ZEGY submitted 2017-03-29 math.CO math.AG

classification math.COmath.AG
keywords latticepolarizationsanalyzedbivariateborelcombinatoricsexploredfound
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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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Cited by 1 Pith paper

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  1. Matchings in Corona graph and classical symmetric varieties

    math.CO 2025-05 conditional novelty 7.0 of 10

    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.

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