# Enumeration of Standard Young Tableaux

@article{Adin2014EnumerationOS, title={Enumeration of Standard Young Tableaux}, author={Ron M. Adin and Yuval Roichman}, journal={arXiv: Combinatorics}, year={2014} }

Question 1.1. What is the total number of resulting configurations? How many configurations are there of any particular shape? In order to answer these questions, at least partially, recall the symmetric group Sn of all permutations of the numbers 1, . . . , n. An involution is a permutation π ∈ Sn such that π is the identity permutation. Theorem 1.2. The total number of configurations of n balls is equal to the number of involutions in the symmetric group Sn. Theorem 1.2 may be traced back to…

## 10 Citations

### Enumeration of Tableaux of Unusual Shapes

- Mathematics
- 2022

In this thesis we enumerate standard young tableaux (SYT) of certain truncated skew shapes, which we call battery shapes. This is motivated by a chess problem. In an enumerative chess problem, the…

### Deriving constant coefficient linear recurrences for enumerating standard Young tableaux of periodic shape.

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The enumeration of several classes of standard Young tableaux are known. However, there are standard Young tableaux of some shapes whose enumeration is still not yet as well known. In this paper, we…

### Commutation Classes of the Reduced Words for the Longest Element of Sn

- MathematicsElectron. J. Comb.
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Using the standard Coxeter presentation for the symmetric group $\mathfrak{S}_{n}$, two reduced expressions for the same group element $\textsf{w}$ are said to be commutationally equivalent if one…

### Recurrence Relations for Wronskian Hermite Polynomials

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We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees…

### Limit shapes of large skew Young tableaux and a modification of the TASEP process

- Mathematics
- 2020

We present a survey of points of view on the problem of the asymptotic shape of a path between two large Young diagrams, and introduce a modification of the TASEP process related to it. This…

### Bounds on Kronecker and $q$-binomial coefficients

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We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend…

### Multiport based teleportation -- protocol and its performance

- Computer Science
- 2020

A lower bound on the performance of the protocol, measured in the entanglement fidelity, is derived using equivalence between the teleportation process and state discrimination task and it is obtained that maximal number of faithfully teleported systems differs qualitatively in deterministic and probabilistic scheme.

### Optimal Multi-port-based Teleportation Schemes

- Computer ScienceQuantum
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In this paper, we introduce optimal versions of a recently studied multi-port based teleportation scheme. We fully characterize probabilistic and deterministic case by presenting expressions for the…

### Multiport based teleportation - transmission of a large amount of quantum information

- Computer Science, PhysicsQuantum
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The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information.

### Enumeration of Standard Young Tableaux of Shifted Strips with Constant Width

- MathematicsElectron. J. Comb.
- 2017

Using of the integral method this paper derives the recurrence relations of g_{3,n}$, g_{n,4} and g_{ n,5} respectively, which is the $(2n-1)$-st Pell number.

## References

SHOWING 1-10 OF 143 REFERENCES

### Descent sets on 321-avoiding involutions and hook decompositions of partitions

- MathematicsJ. Comb. Theory, Ser. A
- 2014

### Asymptotics of Plancherel measures for symmetric groups

- Mathematics
- 1999

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a…

### Shifted tableaux, schur Q-functions, and a conjecture of R. Stanley

- MathematicsJ. Comb. Theory, Ser. A
- 1987

### Arc permutations

- Mathematics
- 2012

Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. This paper studies combinatorial properties and structures on these permutations. First, both…

### Enumeration of lattice paths and generating functions for skew plane partitions

- Mathematics
- 1989

Abstractn-dimensional lattice paths not touching the hyperplanesXi−Xi+1=−1,i=1,2,...,n, are counted by four different statistics, one of which is MacMahon's major index. By a reflection-like proof,…

### Characters of symmetric groups: sharp bounds and applications

- Mathematics
- 2008

We provide new estimates on character values of symmetric groups which hold for all characters and which are in some sense best possible. It follows from our general bound that if a permutation σ∈Sn…

### On Inversions in Standard Young Tableaux

- Mathematics

In this work, we present the inversion number of a standard Young tableau, and determine its distribution over certain sets of standard Young tableaux. Specifically, the work determines the…