Why is the count for labelled sets just 1 in the EGF $e^x = sum 1 cdot frac{x^n}{n!}$?
I have been reading up on species theory and generating functions and I haven't been able to get my head around this. Shouldn't the count for labelled sets still be $n!$ since we are still labelling the elements. This leads to another question: What does a count of $frac{1}{n!}$ for unlabelled sets mean?
This is such a beautiful result yet doesn't seem consistent.
combinatorics generating-functions
asked Nov 27 '18 at 9:17
Michael Hong
293
add a comment |
I have been reading up on species theory and generating functions and I haven't been able to get my head around this. Shouldn't the count for labelled sets still be $n!$ since we are still labelling the elements. This leads to another question: What does a count of $frac{1}{n!}$ for unlabelled sets mean?
This is such a beautiful result yet doesn't seem consistent.
combinatorics generating-functions
asked Nov 27 '18 at 9:17
Michael Hong
293
add a comment |
I have been reading up on species theory and generating functions and I haven't been able to get my head around this. Shouldn't the count for labelled sets still be $n!$ since we are still labelling the elements. This leads to another question: What does a count of $frac{1}{n!}$ for unlabelled sets mean?
This is such a beautiful result yet doesn't seem consistent.
combinatorics generating-functions
asked Nov 27 '18 at 9:17
Michael Hong
293
I have been reading up on species theory and generating functions and I haven't been able to get my head around this. Shouldn't the count for labelled sets still be $n!$ since we are still labelling the elements. This leads to another question: What does a count of $frac{1}{n!}$ for unlabelled sets mean?
This is such a beautiful result yet doesn't seem consistent.
combinatorics generating-functions
combinatorics generating-functions
asked Nov 27 '18 at 9:17
Michael Hong
293
asked Nov 27 '18 at 9:17
Michael Hong
293
asked Nov 27 '18 at 9:17
Michael Hong
293
asked Nov 27 '18 at 9:17
Michael Hong
293
asked Nov 27 '18 at 9:17
Michael Hong
293
293
add a comment |
add a comment |
0
active
oldest
votes
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
});
}
});
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%2f3015542%2fwhy-is-the-count-for-labelled-sets-just-1-in-the-egf-ex-sum-1-cdot-fracx%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3015542%2fwhy-is-the-count-for-labelled-sets-just-1-in-the-egf-ex-sum-1-cdot-fracx%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
