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1. Definition & Example

There are two standard ways to denote $\pi \in \mathfrak{S}_n$.


The six permutations of size 3







2. FindStat representation and coverage

3. Additional information

3.1. The Rothe diagram of a permutation

3.2. The Lehmer code for a permutation

3.3. Special classes of permutations

3.3.1. Pattern-avoiding permutations

$$ \#\big\{ \sigma \in \mathfrak{S}_n : \sigma \text{ avoids } \tau \big\} = \frac{1}{n+1}\binom{2n}{n}, $$

where we set $t_0=0$ and $t_k=n+1$.

3.4. Classes of permutations in Schubert calculus

The following classes of permutations play important roles in the theory of Schubert polynomials, see e.g. [Man01, Section 2.2]. A permutation $\sigma \in \mathfrak{S}_n$ is called

3.5. Properties

3.6. Remarks

4. References

5. Sage examples