Subsets of Reduced Latin Squares of a Given Order
$begingroup$
I would like to know conventional methods for specifying subsets of reduced latin squares of a given order that have certain properties under multiplication.
#1) It seems redundant to indicate that reduced latin squares must show the idempotence of the first element; is this accurate?
#2) Is there a convention for indicating that a square exhibits commutativity such that the values at a given column and row are equal to those at the inversion of its column and row (e.g., the value at row three, column two is the same as the one at row two, column three)?
#3) As with item #1, would indicating that the squares exhibit commutativity also make redundant specifying the idempotence of the first element?
combinatorics elementary-set-theory terminology latin-square
$endgroup$
add a comment |
$begingroup$
I would like to know conventional methods for specifying subsets of reduced latin squares of a given order that have certain properties under multiplication.
#1) It seems redundant to indicate that reduced latin squares must show the idempotence of the first element; is this accurate?
#2) Is there a convention for indicating that a square exhibits commutativity such that the values at a given column and row are equal to those at the inversion of its column and row (e.g., the value at row three, column two is the same as the one at row two, column three)?
#3) As with item #1, would indicating that the squares exhibit commutativity also make redundant specifying the idempotence of the first element?
combinatorics elementary-set-theory terminology latin-square
$endgroup$
add a comment |
$begingroup$
I would like to know conventional methods for specifying subsets of reduced latin squares of a given order that have certain properties under multiplication.
#1) It seems redundant to indicate that reduced latin squares must show the idempotence of the first element; is this accurate?
#2) Is there a convention for indicating that a square exhibits commutativity such that the values at a given column and row are equal to those at the inversion of its column and row (e.g., the value at row three, column two is the same as the one at row two, column three)?
#3) As with item #1, would indicating that the squares exhibit commutativity also make redundant specifying the idempotence of the first element?
combinatorics elementary-set-theory terminology latin-square
$endgroup$
I would like to know conventional methods for specifying subsets of reduced latin squares of a given order that have certain properties under multiplication.
#1) It seems redundant to indicate that reduced latin squares must show the idempotence of the first element; is this accurate?
#2) Is there a convention for indicating that a square exhibits commutativity such that the values at a given column and row are equal to those at the inversion of its column and row (e.g., the value at row three, column two is the same as the one at row two, column three)?
#3) As with item #1, would indicating that the squares exhibit commutativity also make redundant specifying the idempotence of the first element?
combinatorics elementary-set-theory terminology latin-square
combinatorics elementary-set-theory terminology latin-square
asked Dec 8 '18 at 14:40
bblohowiakbblohowiak
1049
1049
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%2f3031184%2fsubsets-of-reduced-latin-squares-of-a-given-order%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.
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%2f3031184%2fsubsets-of-reduced-latin-squares-of-a-given-order%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