the following four questions: Question 1. Apply the RSK algorithm to the followi

Question

the following four questions:
Question 1. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters:
w=561874923
Question 2. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters: u=329478165
Question 3. Apply the RSK algorithm to the bijection that is inverse to the permutation u in Question 2.
Question 4. What permutation in the symmetric group on 13 "letters" gets sent to the following pair of standard Young tableux (P,Q) under the RSK algorithm?



I attached the original Marica-Schoenheim paper. Note when discussing the counterexample to the more general conjecture, they write "5" when they should have written "6."
The difference between square-free positive integers and general positive integers is the difference between sets and multisets. It turns out you can do almost the entire Marica-Schoenheim proof with multisets! Obviously not the entire proof, since the Marica-Schoenheim proof evidently fails for multisets. I include it in case you can tinker with it and make a modified proof for the original Graham conjecture, which is now a theorem---I attach a paper by the two people who proved it. A short proof would be, I think, a big result.
Is there a simpler proof? One that doesn't involved computer searches for large prime numbers? This is probably hard, since the original conjecture took some 26 years to prove, but it would be a big deal if you could do it!
Note that a mathematician did generalize the Marica-Schoenheim Theorem to distributive lattices. It's not quite a generalization that would imply the Graham conjecture, but, again, maybe you can someday see how it would get us there.... That paper also has some open questions. (I am not saying those are major questions to work on.)
the following four questions:
Question 1. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters:
w=561874923
Question 2. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters: u=329478165
Question 3. Apply the RSK algorithm to the bijection that is inverse to the permutation u in Question 2.
Question 4. What permutation in the symmetric group on 13 "letters" gets sent to the following pair of standard Young tableux (P,Q) under the RSK algorithm?



I attached the original Marica-Schoenheim paper. Note when discussing the counterexample to the more general conjecture, they write "5" when they should have written "6."
The difference between square-free positive integers and general positive integers is the difference between sets and multisets. It turns out you can do almost the entire Marica-Schoenheim proof with multisets! Obviously not the entire proof, since the Marica-Schoenheim proof evidently fails for multisets. I include it in case you can tinker with it and make a modified proof for the original Graham conjecture, which is now a theorem---I attach a paper by the two people who proved it. A short proof would be, I think, a big result.
Is there a simpler proof? One that doesn't involved computer searches for large prime numbers? This is probably hard, since the original conjecture took some 26 years to prove, but it would be a big deal if you could do it!
Note that a mathematician did generalize the Marica-Schoenheim Theorem to distributive lattices. It's not quite a generalization that would imply the Graham conjecture, but, again, maybe you can someday see how it would get us there.... That paper also has some open questions. (I am not saying those are major questions to work on.)
the following four questions:
Question 1. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters:
w=561874923
Question 2. Apply the RSK algorithm to the following permutation in the symmetric group on 9 letters: u=329478165
Question 3. Apply the RSK algorithm to the bijection that is inverse to the permutation u in Question 2.
Question 4. What permutation in the symmetric group on 13 "letters" gets sent to the following pair of standard Young tableux (P,Q) under the RSK algorithm?



I attached the original Marica-Schoenheim paper. Note when discussing the counterexample to the more general conjecture, they write "5" when they should have written "6."
The difference between square-free positive integers and general positive integers is the difference between sets and multisets. It turns out you can do almost the entire Marica-Schoenheim proof with multisets! Obviously not the entire proof, since the Marica-Schoenheim proof evidently fails for multisets. I include it in case you can tinker with it and make a modified proof for the original Graham conjecture, which is now a theorem---I attach a paper by the two people who proved it. A short proof would be, I think, a big result.
Is there a simpler proof? One that doesn't involved computer searches for large prime numbers? This is probably hard, since the original conjecture took some 26 years to prove, but it would be a big deal if you could do it!
Note that a mathematician did generalize the Marica-Schoenheim Theorem to distributive lattices. It's not quite a generalization that would imply the Graham conjecture, but, again, maybe you can someday see how it would get us there.... That paper also has some open questions. (I am not saying those are major questions to work on.)

Explanation / Answer

Let us be a set of n element a one -one onto mapping from a s to s is called permutation on s

The set of all permutation is denoted by sn

Representation of permutation : s=[a1,a2,a3......an]

Let f€sn and f(a1)=b1

f(a2)=b2.......f(an)=bn where bi€s

Permutation group or symmetric group

Let s be set of n element the set of all one one onto mapping from s to s from a group with respect to the composition of mapping. The set of permutation mapping is called permutation group or symmetric group and denoted by sn

N=9

S9= 9!= 9×8×7×6×5×4×3×2×1=362880

We have 362880 group of s9 permutation

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