# 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

### A continuous family of partition statistics equidistributed with length

- MathematicsJ. Comb. Theory, Ser. A
- 2009

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

- Mathematics
- 1997

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

- Mathematics
- 1975

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

- Computer ScienceElectron. 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

- Mathematics
- 2005

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

- Mathematics
- 2012

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

- Mathematics
- 2013

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…

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

- Jiaoyang Huang, Department of Mathematics