All Questions
Tagged with algebraic-combinatorics permutations
9
questions
3
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Given a transitive and faithful permutation group $G$, is each set of syntactically transitive permutations connected by another permutation in $G$?
$G$ is a permutation group of degree $n \geq 4$ which acts transitively and faithfully on a set $X$ with $|X| = n$.
Given indices $i < j < k \leq n$, elements $\alpha \neq \beta \neq \gamma \in ...
- 317
3
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0
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31
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Decidability of Wilf Equivalence
I have seen a lot of papers discussing whether various permutation classes are Wilf equivalent to each other. I wonder if we could solve such problems in general with computers.
More rigorously, let $\...
- 9,080
1
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1
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the number of sequences is equal to the number of permutations
Consider the product
$A_n = \left\{1\right\} \times \left\{1,2\right\} \times \cdots \times \left\{1,2,\ldots,n\right\}$.
For $\sigma = (a_1, a_2, . . . , a_n) \in A_n$, define the set of descents
$\...
user732679
2
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0
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63
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When does multiplying by an involution increase the Bruhat Order in the Symmetric Group?
Let $w \in \mathrm{Sym}(n)$ for some positive integer $n$. Let $r$ be an involution in $\mathrm{Sym}(n)$, and write it as the product of disjoint transpositions like so: $$r = \prod_{i=1}^k (a_i,b_i) $...
- 317
1
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Number for ways to arrange 10 distinct object into 4 distinct boxes
What is the number of ways to arrange 10 distinct objects into 4 distinct boxes, where each box hold no more than 4 objects
This question was asked earlier today, but has been deleted, I don't know ...
1
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0
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134
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Permutations That Are Conjugate with an Element From Stabilizer of Another Permutation
We know that permutations, elements of the symmetric group on a finite set with n elements, are conjugate iff they have the same cycle structure.
My question is that given two permutations that are ...
- 149
4
votes
1
answer
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Prove the bijections between the following $(p,q,r)$-shuffles
I am reading the book "From Calculus to Cohomology: De Rham cohomology and characteristic classes"
Let $p, q, r$ be nonnegative integers.
It says, (for those who own the book, on pg 10) without ...
- 1,048
3
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1
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484
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What is the following way of indexing permutations called?
I'm sure this is well-known but I don't know where to look in order to find it.
Consider a permutation, e.g. $\sigma = 2 1 4 3$ in one-line notation. This corresponds to a monotone triangle via
\...
- 24.9k
4
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Use of rook polynomials
Use rook polynomials to count the number of permutations of $(1,2,3,4)$ in which $1$ is not in the second position, $2$ is not in the fourth position, and $3$ is not in the first or fourth position. ...
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