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Title: Positroid Catalan numbers

Given a (bounded affine) permutationff, we study thepositroid Catalan numberCfC_fdefined to be the torus-equivariant Euler characteristic of the associated open positroid variety. We introduce a class ofrepetition-free permutationsand show that the corresponding positroid Catalan numbers count Dyck paths avoiding a convex subset of the rectangle. We show that any convex subset appears in this way. Conjecturally, the associatedq,tq,t-polynomials coincide with thegeneralizedq,tq,t-Catalan numbersthat recently appeared in relation to the shuffle conjecture, flag Hilbert schemes, and Khovanov–Rozansky homology of Coxeter links.

 
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NSF-PAR ID:
10499665
Author(s) / Creator(s):
;
Publisher / Repository:
American Mathematical Society (AMS)
Date Published:
Journal Name:
Communications of the American Mathematical Society
Volume:
4
Issue:
8
ISSN:
2692-3688
Format(s):
Medium: X Size: p. 357-386
Size(s):
["p. 357-386"]
Sponsoring Org:
National Science Foundation
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