• Corpus ID: 14792596

Partition Statistics Equidistributed with the Number of Hook Difference One Cells

@article{Huang2014PartitionSE,
  title={Partition Statistics Equidistributed with the Number of Hook Difference One Cells},
  author={Jiaoyang Huang and Andrew Senger and Peter Wear and Tianqi Wu},
  journal={arXiv: Combinatorics},
  year={2014}
}
Let $\lambda$ be a partition, viewed as a Young diagram. We define the hook difference of a cell of $\lambda$ to be the difference of its leg and arm lengths. Define $h_{1,1}(\lambda)$ to be the number of cells of $\lambda$ with hook difference one. In the paper of Buryak and Feigin (arXiv:1206.5640), algebraic geometry is used to prove a generating function identity which implies that $h_{1,1}$ is equidistributed with $a_2$, the largest part of a partition that appears at least twice, over the… 

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References

SHOWING 1-10 OF 15 REFERENCES

The Family G T of Graded Artinian Quotients of k[x, y] of Given Hilbert Function

Abstract Let R = k[x, y] be the polynomial ring over an algebraically closed field k. Let Tbe a sequence of nonnegative integers that occurs as the Hilbert function of a length-nArtinian quotient of

Rook theory. I. Rook equivalence of Ferrers boards

We introduce a new tool, the factorial polynomials, to study rook equivalence of Ferrers boards. We provide a set of invariants for rook equivalence as well as a very simple algorithm for deciding

The On-Line Encyclopedia of Integer Sequences

  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.

A Combinatorial Study on Quiver Varieties

This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a

Generating Series of the Poincaré Polynomials of Quasihomogeneous Hilbert Schemes

In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We

A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes

In a recent paper, the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an

q-Catalan Numbers

Massachusetts Institute of Technology E-mail address: jiaoyang@mit

  • Jiaoyang Huang, Department of Mathematics