Compactified Jacobians and q,t-Catalan numbers, II

@article{Gorsky2011CompactifiedJA,
  title={Compactified Jacobians and q,t-Catalan numbers, II},
  author={Evgeny Gorsky and Mikhail Mazin},
  journal={Journal of Algebraic Combinatorics},
  year={2011},
  volume={39},
  pages={153-186}
}

Limits of Modified Higher q,t-Catalan Numbers

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

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

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

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

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

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

Recursions for rational q, t-Catalan numbers

The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link

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

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.

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
...

References

SHOWING 1-10 OF 45 REFERENCES

Compactified Jacobians and q,t-Catalan numbers, II

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

A proof of the q, t-Catalan positivity conjecture

Torus knots and the rational DAHA

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

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

Gorenstein curves and symmetry of the semigroup of values

LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in [7] proves thatO is a Gorenstein ring if and only if S is symmetrical. In this paper we give a

Conjectured Statistics for the Higher q, t-Catalan Sequences

  • N. Loehr
  • Mathematics
    Electron. J. Comb.
  • 2005
This article describes conjectured combinatorial interpretations for the higher $q,t$-Catalan sequences introduced by Garsia and Haiman, which arise in the theory of symmetric functions and Macdonald

Counting rational curves on K3 surfaces

The aim of these notes is to explain the remarkable formula found by Yau and Zaslow to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families

The value-semigroup of a one-dimensional Gorenstein ring

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

Vanishing theorems and character formulas for the Hilbert scheme of points in the plane

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,