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Limits of Modified Higher q,t-Catalan Numbers
- MathematicsElectron. J. Comb.
- 2013
The limits of several versions of the modified higher $q,t$-Catalan numbers are computed and it is shown that these limits equal the generating function for integer partitions.
2 7 M ay 2 01 9 GENERALIZED q , t-CATALAN NUMBERS
- Mathematics
- 2019
Recent work of the first author, Negut, and Rasmussen, and of Oblomkov and Rozansky in the context of Khovanov–Rozansky knot homology produces a family of polynomials in q and t labeled by integer…
Generalized $q,t$-Catalan numbers
- Mathematics
- 2020
Author(s): Gorsky, Eugene; Hawkes, Graham; Schilling, Anne; Rainbolt, Julianne | Abstract: Recent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of…
q;t-Catalan numbers
- Mathematics
- 2013
The q;t-Catalan numbers can be dened using rational functions, geometry related to Hilbert schemes, symmetric functions, representation theory, Dyck paths, partition statistics, or Dyck words. After…
Torus knots and the rational DAHA
- Mathematics
- 2014
Author(s): Gorsky, E; Oblomkov, A; Rasmussen, J; Shende, V | Abstract: © 2014. We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m;n) torus knot from the unique…
Combinatorics of certain higher q,t-Catalan polynomials: chains, joint symmetry, and the Garsia–Haiman formula
- Mathematics
- 2012
The higher q,t-Catalan polynomial $C^{(m)}_{n}(q,t)$ can be defined combinatorially as a weighted sum of lattice paths contained in certain triangles, or algebraically as a complicated sum of…
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
- Mathematics
- 2018
Author(s): Oblomkov, A; Rasmussen, J; Shende, V; Gorsky, E | Abstract: © 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of the…
FOR DAHA SUPERPOLYNOMIALS AND PLANE CURVE SINGULARITIES
- Mathematics
- 2018
Stable Khovanov-Rozansky polynomials of algebraic knots are expected to coincide with certain generating functions, superpolynomials, of nested Hilbert schemes and flagged Jacobian factors of the…
expansions and the rational shuffle theorem.
- Mathematics
- 2022
The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). 789–800 (2014; Zbl 1393.05275)] gave a combinatorial proof of the Schur function expansion of Q 2 , 2 n +1 (1) and Q 2 n…
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We continue the study of the rational-slope generalized q,t-Catalan numbers cm,n(q,t). We describe generalizations of the bijective constructions of J. Haglund and N. Loehr and use them to prove a…
Torus knots and the rational DAHA
- Mathematics
- 2014
Author(s): Gorsky, E; Oblomkov, A; Rasmussen, J; Shende, V | Abstract: © 2014. We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m;n) torus knot from the unique…
Combinatorics of certain higher q,t-Catalan polynomials: chains, joint symmetry, and the Garsia–Haiman formula
- Mathematics
- 2012
The higher q,t-Catalan polynomial $C^{(m)}_{n}(q,t)$ can be defined combinatorially as a weighted sum of lattice paths contained in certain triangles, or algebraically as a complicated sum of…
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In a conversation about [4], 0. Zariski indicated to the author that there should be a relation between Gorenstein rings and symmetric value-semigroups, possibly allowing a new proof for a result of…
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Abstract.In an earlier paper [14], we showed that the Hilbert scheme of points in the plane Hn=Hilbn(ℂ2) can be identified with the Hilbert scheme of regular orbits ℂ2n//Sn. Using this result,…