Cluster algebra associated to a d-gon
up vote
0
down vote
favorite
Recently I have been doing some reading on cluster algebras, for example this. When defining the cluster algebras associated to a $d$-gon, they claim that the cluster and coefficient variables of $A_{d−3}$ are in bijection with the diagonals and sides of the $d$-gon, and the clusters are in bijection with triangulations of the $d$-gon, but I'm not really sure how to prove it and I don't think this is simply just the matter of counting.
I'd appreciate any ideas or references, or both.
abstract-algebra cluster-algebra
asked Nov 22 at 11:34
amator2357
76
add a comment |
up vote
0
down vote
favorite
Recently I have been doing some reading on cluster algebras, for example this. When defining the cluster algebras associated to a $d$-gon, they claim that the cluster and coefficient variables of $A_{d−3}$ are in bijection with the diagonals and sides of the $d$-gon, and the clusters are in bijection with triangulations of the $d$-gon, but I'm not really sure how to prove it and I don't think this is simply just the matter of counting.
I'd appreciate any ideas or references, or both.
abstract-algebra cluster-algebra
asked Nov 22 at 11:34
amator2357
76
1
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Recently I have been doing some reading on cluster algebras, for example this. When defining the cluster algebras associated to a $d$-gon, they claim that the cluster and coefficient variables of $A_{d−3}$ are in bijection with the diagonals and sides of the $d$-gon, and the clusters are in bijection with triangulations of the $d$-gon, but I'm not really sure how to prove it and I don't think this is simply just the matter of counting.
I'd appreciate any ideas or references, or both.
abstract-algebra cluster-algebra
asked Nov 22 at 11:34
amator2357
76
Recently I have been doing some reading on cluster algebras, for example this. When defining the cluster algebras associated to a $d$-gon, they claim that the cluster and coefficient variables of $A_{d−3}$ are in bijection with the diagonals and sides of the $d$-gon, and the clusters are in bijection with triangulations of the $d$-gon, but I'm not really sure how to prove it and I don't think this is simply just the matter of counting.
I'd appreciate any ideas or references, or both.
abstract-algebra cluster-algebra
abstract-algebra cluster-algebra
asked Nov 22 at 11:34
amator2357
76
asked Nov 22 at 11:34
amator2357
76
asked Nov 22 at 11:34
amator2357
76
asked Nov 22 at 11:34
amator2357
76
asked Nov 22 at 11:34
amator2357
76
76
1
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53
add a comment |
1
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53
1
1
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53
add a comment |
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',
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%2f3009027%2fcluster-algebra-associated-to-a-d-gon%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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%2f3009027%2fcluster-algebra-associated-to-a-d-gon%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
1
Section 2.2 of the linked paper is a proof of the property you describe, if you're having problem with an aspect of that proof you should describe more clearly which step you're having trouble with.
– Christopher
Nov 23 at 16:53