Show that for all n ∈ N, L(n) < $2^n$ The Next CEO of Stack OverflowProof that $sqrt5$ is irrationalHow do I show that two sets are equal.Show that if $f:Ato B$ is a bijection then $f^-1$ is a surjectionShow root of unity and orderLet $G$ be a group of order 1210 with a subgroup $H$ of order 121. Show that every element of order 11 is in $H$How to show that the fabius function is nowhere analytic?Period of the decimal expression for the rational number $frac1n$ is at most $n-1$Show that variable lies in specific intervalProof: Well defined multiplication in groupsShow that $gcd(a, 0)$ exists and equals $|a|$ for all $a$ in $mathbb Z$
% symbol leads to superlong (forever?) compilations
How easy is it to start Magic from scratch?
Rotate a column
Why do professional authors make "consistency" mistakes? And how to avoid them?
Only print output after finding pattern
How do I construct this japanese bowl?
How to start emacs in "nothing" mode (`fundamental-mode`)
How do I get the green key off the shelf in the Dobby level of Lego Harry Potter 2?
What does this shorthand mean?
What do "high sea" and "carry" mean in this sentence?
Are there languages with no euphemisms?
Anatomically Correct Strange Women In Ponds Distributing Swords
Unreliable Magic - Is it worth it?
Why were Madagascar and New Zealand discovered so late?
What is the purpose of the Evocation wizard's Potent Cantrip feature?
How can I get through very long and very dry, but also very useful technical documents when learning a new tool?
Horror movie/show or scene where a horse creature opens its mouth really wide and devours a man in a stables
Anatomically Correct Mesopelagic Aves
Trouble understanding the speech of overseas colleagues
WOW air has ceased operation, can I get my tickets refunded?
What happens if you roll doubles 3 times then land on "Go to jail?"
Where to find order of arguments for default functions
How to get regions to plot as graphics
Should I tutor a student who I know has cheated on their homework?
Show that for all n ∈ N, L(n)
The Next CEO of Stack OverflowProof that $sqrt5$ is irrationalHow do I show that two sets are equal.Show that if $f:Ato B$ is a bijection then $f^-1$ is a surjectionShow root of unity and orderLet $G$ be a group of order 1210 with a subgroup $H$ of order 121. Show that every element of order 11 is in $H$How to show that the fabius function is nowhere analytic?Period of the decimal expression for the rational number $frac1n$ is at most $n-1$Show that variable lies in specific intervalProof: Well defined multiplication in groupsShow that $gcd(a, 0)$ exists and equals $|a|$ for all $a$ in $mathbb Z$
$begingroup$
Im confused at what this question means and how to answer it.
Also unsure on how to do the following question
Show that L(n) $geq fracn2$· $(fracn2 −1)$ for $n ∈ N$
The $L(n)$ confuses me.
Thanks !
Edit: $L(n)$ (Landau’s function) is defined for every $n ∈ N$ to be the largest order of an element of Sn.
proof-writing
edited yesterday
Anirban Niloy
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Im confused at what this question means and how to answer it.
Also unsure on how to do the following question
Show that L(n) $geq fracn2$· $(fracn2 −1)$ for $n ∈ N$
The $L(n)$ confuses me.
Thanks !
Edit: $L(n)$ (Landau’s function) is defined for every $n ∈ N$ to be the largest order of an element of Sn.
proof-writing
edited yesterday
Anirban Niloy
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday
add a comment |
$begingroup$
Im confused at what this question means and how to answer it.
Also unsure on how to do the following question
Show that L(n) $geq fracn2$· $(fracn2 −1)$ for $n ∈ N$
The $L(n)$ confuses me.
Thanks !
Edit: $L(n)$ (Landau’s function) is defined for every $n ∈ N$ to be the largest order of an element of Sn.
proof-writing
edited yesterday
Anirban Niloy
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Im confused at what this question means and how to answer it.
Also unsure on how to do the following question
Show that L(n) $geq fracn2$· $(fracn2 −1)$ for $n ∈ N$
The $L(n)$ confuses me.
Thanks !
Edit: $L(n)$ (Landau’s function) is defined for every $n ∈ N$ to be the largest order of an element of Sn.
proof-writing
proof-writing
edited yesterday
Anirban Niloy
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Anirban Niloy
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Anirban Niloy
8411318
edited yesterday
Anirban Niloy
8411318
edited yesterday
Anirban Niloy
8411318
8411318
asked yesterday
AnonymousAnonymous
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
AnonymousAnonymous
11
asked yesterday
AnonymousAnonymous
11
11
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Anonymous is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday
add a comment |
2
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday
2
2
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
For the second question: If $n=2k$ one can do the product of two disjoint cycles, one of length $k$ and one of length $k-1.$ (fix remaining spot.) Since order is lcm of cycle lengths this has order $k(k-1)=(n/2)(n/2-1).$
If $n=2k+1$ one can do the product of two cycles, one of length k and one of length $k+1.$ This has order $k(k+1)>(n/2)(n/2-1).$
I don't see how to do the first question, but the bound seems relatively high, I'd expect a better bound but don't see how to get it.
answered yesterday
coffeemathcoffeemath
2,9071415
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Anonymous is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3164324%2fshow-that-for-all-n-%25e2%2588%2588-n-ln-2n%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
For the second question: If $n=2k$ one can do the product of two disjoint cycles, one of length $k$ and one of length $k-1.$ (fix remaining spot.) Since order is lcm of cycle lengths this has order $k(k-1)=(n/2)(n/2-1).$
If $n=2k+1$ one can do the product of two cycles, one of length k and one of length $k+1.$ This has order $k(k+1)>(n/2)(n/2-1).$
I don't see how to do the first question, but the bound seems relatively high, I'd expect a better bound but don't see how to get it.
answered yesterday
coffeemathcoffeemath
2,9071415
$endgroup$
add a comment |
$begingroup$
For the second question: If $n=2k$ one can do the product of two disjoint cycles, one of length $k$ and one of length $k-1.$ (fix remaining spot.) Since order is lcm of cycle lengths this has order $k(k-1)=(n/2)(n/2-1).$
If $n=2k+1$ one can do the product of two cycles, one of length k and one of length $k+1.$ This has order $k(k+1)>(n/2)(n/2-1).$
I don't see how to do the first question, but the bound seems relatively high, I'd expect a better bound but don't see how to get it.
answered yesterday
coffeemathcoffeemath
2,9071415
$endgroup$
add a comment |
$begingroup$
For the second question: If $n=2k$ one can do the product of two disjoint cycles, one of length $k$ and one of length $k-1.$ (fix remaining spot.) Since order is lcm of cycle lengths this has order $k(k-1)=(n/2)(n/2-1).$
If $n=2k+1$ one can do the product of two cycles, one of length k and one of length $k+1.$ This has order $k(k+1)>(n/2)(n/2-1).$
I don't see how to do the first question, but the bound seems relatively high, I'd expect a better bound but don't see how to get it.
answered yesterday
coffeemathcoffeemath
2,9071415
$endgroup$
For the second question: If $n=2k$ one can do the product of two disjoint cycles, one of length $k$ and one of length $k-1.$ (fix remaining spot.) Since order is lcm of cycle lengths this has order $k(k-1)=(n/2)(n/2-1).$
If $n=2k+1$ one can do the product of two cycles, one of length k and one of length $k+1.$ This has order $k(k+1)>(n/2)(n/2-1).$
I don't see how to do the first question, but the bound seems relatively high, I'd expect a better bound but don't see how to get it.
answered yesterday
coffeemathcoffeemath
2,9071415
answered yesterday
coffeemathcoffeemath
2,9071415
answered yesterday
coffeemathcoffeemath
2,9071415
answered yesterday
coffeemathcoffeemath
2,9071415
2,9071415
add a comment |
add a comment |
Anonymous is a new contributor. Be nice, and check out our Code of Conduct.
Anonymous is a new contributor. Be nice, and check out our Code of Conduct.
Anonymous is a new contributor. Be nice, and check out our Code of Conduct.
Anonymous is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3164324%2fshow-that-for-all-n-%25e2%2588%2588-n-ln-2n%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
How is $L(n)$ defined?
$endgroup$
– Dietrich Burde
yesterday
$begingroup$
I can't see some characters in your question, they look like empty boxes in my browser: i.stack.imgur.com/362ag.png What are they?
$endgroup$
– CiaPan
yesterday
$begingroup$
should be fine now, I can see the characters in the question clearly on mine, where can you see the boxes ?
$endgroup$
– Anonymous
yesterday
$begingroup$
Boxes still there on my feed.
$endgroup$
– coffeemath
yesterday
$begingroup$
where are the boxes
$endgroup$
– Anonymous
yesterday