The Selberg integral and Young books

@article{Kim2014TheSI,
  title={The Selberg integral and Young books},
  author={Jang Soo Kim and Suho Oh},
  journal={J. Comb. Theory, Ser. A},
  year={2014},
  volume={145},
  pages={1-24}
}
  • J. KimSuho Oh
  • Published 4 September 2014
  • Mathematics
  • J. Comb. Theory, Ser. A

Hook formulas for skew shapes III. Multivariate and product formulas

We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing

Three enumeration formulas of standard Young tableaux of truncated shapes

Abstract In this paper we consider the enumeration of three kinds of standard Young tableaux (SYT) of truncated shapes by use of the method of multiple integrals. A product formula for the number of

On q-integrals over order polytopes

Weight multiplicities and Young tableaux through affine crystals

The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit

Asymptotic algebraic combinatorics

Algebraic Combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies

Hidden Symmetries of Weighted Lozenge Tilings

It is proved that this weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) is symmetric for large families of regions.

Asymptotics for skew standard Young tableaux via bounds for characters

We are interested in the asymptotics of the number of standard Young tableaux $f^{\lambda/\mu}$ of a given skew shape $\lambda/\mu$. We mainly restrict ourselves to the case where both diagrams are

References

SHOWING 1-10 OF 18 REFERENCES

The Selberg integral and Young books (Extended Abstract)

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combina- torial interpretation of the Selberg integral in terms of permutations. In this paper, new

The importance of the Selberg integral

It has been remarked that a fair measure of the impact of Atle Selberg’s work is the number of mathematical terms that bear his name. One of these is the Selberg integral, an n-dimensional

Tableaux and plane partitions of truncated shapes

Enumerative Combinatorics: Volume 1

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of

Evaluating the Numbers of some Skew Standard Young Tableaux of Truncated Shapes

  • Ping Sun
  • Mathematics
    Electron. J. Comb.
  • 2015
The number of standard Young tableaux (SYT) is evaluated by the methods of multiple integrals and combinatorial summations.

Enumeration of Standard Young Tableaux of certain Truncated Shapes

Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner,

The Hook Graphs of the Symmetric Group

Each irreducible representation [λ] of the symmetric group S n may be identified by a partition [λ] of n into non-negative integral parts λ1 ≥ λ2 ≥ … λ n ≥ 0, of which the first λ'j parts are ≥j, or

Permutohedra, Associahedra, and Beyond

The volume and the number of lattice points of the permutohedron Pn are given by certain multivariate polynomials that have remarkable com- binatorial properties. We give 3 dieren t formulas for

Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of