## 81 Citations

### 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…

## References

SHOWING 1-10 OF 45 REFERENCES

### Compactified Jacobians and q,t-Catalan numbers, II

- MathematicsJournal of Algebraic Combinatorics
- 2013

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…

### Gorenstein curves and symmetry of the semigroup of values

- Mathematics
- 1988

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

- MathematicsElectron. 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

- Mathematics
- 1997

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

- Mathematics
- 1970

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

- Mathematics
- 2001

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,…