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Results tagged with permutations
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user 80819
Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.
3
votes
3
answers
185
views
Characterizing (up to permutations) finite sequences of real numbers
characterizing the family of functions $F$ such that for any $f\in F$ the function
$$
c(\lambda) =\sum_{i=1}^{N}f(x_i-\lambda),\;\lambda \in \mathbb{R}
$$
uniquely identifies the sequence $S$ up to element permutations …
- 329
1
vote
0
answers
53
views
Set of vectors closed under restricted permutation operations
I am trying to demonstrate that if $Q=\{P_i\in R^{k\times k},i=1,\cdots,k\}$ is a set of permutations such that:
\begin{eqnarray}
&&\sum_{q=1}^{k}P_q=J\\
&& P_i\circ P_j =\mathbb{0}, i\neq j\\
&& P_iP_j …
- 329
0
votes
0
answers
52
views
Gramian of a permutation group orbit
Suppose that the associated gramian has the following structure:
$$
W^TW=(P_{1}t,\cdots,P_{k}t)
$$
with the set $\{P_{i},i=1,\cdots,k\}$ forming a group of permutations (on $k$ objects) and $t\in R^k$. … an orbit of a permutation group up to an isometry, i.e.
$$
W=UO,\;\;\; O=(\bar{P}_{1}s,\cdots,\bar{P}_{k}s),\;\;\;\;\;\;\;\;U^TU=Id
$$
with the set $\{\bar{P}_{i},i=1,\cdots,k\}$ forming a group of permutations …
- 329