Photo Booth problem
There are $n$ people.
There is a Photo Booth in which they can enter at most $m$ people at one time.
They want to get a picture with all other person together.
Please solve the $F(n,m)$; minimum number of times to get required pictures.
For example, there are people: $A$, $B$, $C$ and $D$, and a Photo Booth in which they can enter at most $3$ people at one time. When they form a group $left{ A, B, C right}$, $left{B, C, D right}$ and $left{A, C, Dright}$, $A$ can get pictures with $B$, $C$ and $D$ ,etc. In this case, $F(4,3)=3$
See also Question of difficult matrix problem, minimum number of times
linear-algebra combinatorics matrices graph-theory
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
add a comment |
There are $n$ people.
There is a Photo Booth in which they can enter at most $m$ people at one time.
They want to get a picture with all other person together.
Please solve the $F(n,m)$; minimum number of times to get required pictures.
For example, there are people: $A$, $B$, $C$ and $D$, and a Photo Booth in which they can enter at most $3$ people at one time. When they form a group $left{ A, B, C right}$, $left{B, C, D right}$ and $left{A, C, Dright}$, $A$ can get pictures with $B$, $C$ and $D$ ,etc. In this case, $F(4,3)=3$
See also Question of difficult matrix problem, minimum number of times
linear-algebra combinatorics matrices graph-theory
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
add a comment |
There are $n$ people.
There is a Photo Booth in which they can enter at most $m$ people at one time.
They want to get a picture with all other person together.
Please solve the $F(n,m)$; minimum number of times to get required pictures.
For example, there are people: $A$, $B$, $C$ and $D$, and a Photo Booth in which they can enter at most $3$ people at one time. When they form a group $left{ A, B, C right}$, $left{B, C, D right}$ and $left{A, C, Dright}$, $A$ can get pictures with $B$, $C$ and $D$ ,etc. In this case, $F(4,3)=3$
See also Question of difficult matrix problem, minimum number of times
linear-algebra combinatorics matrices graph-theory
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
There are $n$ people.
There is a Photo Booth in which they can enter at most $m$ people at one time.
They want to get a picture with all other person together.
Please solve the $F(n,m)$; minimum number of times to get required pictures.
For example, there are people: $A$, $B$, $C$ and $D$, and a Photo Booth in which they can enter at most $3$ people at one time. When they form a group $left{ A, B, C right}$, $left{B, C, D right}$ and $left{A, C, Dright}$, $A$ can get pictures with $B$, $C$ and $D$ ,etc. In this case, $F(4,3)=3$
See also Question of difficult matrix problem, minimum number of times
linear-algebra combinatorics matrices graph-theory
linear-algebra combinatorics matrices graph-theory
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
asked Jan 3 '15 at 16:36
Soft CreamSoft Cream
135
135
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
A $(v,k,t)$ covering is a family of subsets of ${1,2,3dots v}$ such that each subset has $k$ elements and every subset of ${1,2,3dots,v}$ that has exactly $t$ elements is contained in one of the subsets of the family.
What you want to find is the minimal subsets that can be in a ${v,k,2}$ covering. Here is a repository of such coverings.
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
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
});
}
});
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%2f1089811%2fphoto-booth-problem%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
A $(v,k,t)$ covering is a family of subsets of ${1,2,3dots v}$ such that each subset has $k$ elements and every subset of ${1,2,3dots,v}$ that has exactly $t$ elements is contained in one of the subsets of the family.
What you want to find is the minimal subsets that can be in a ${v,k,2}$ covering. Here is a repository of such coverings.
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
add a comment |
A $(v,k,t)$ covering is a family of subsets of ${1,2,3dots v}$ such that each subset has $k$ elements and every subset of ${1,2,3dots,v}$ that has exactly $t$ elements is contained in one of the subsets of the family.
What you want to find is the minimal subsets that can be in a ${v,k,2}$ covering. Here is a repository of such coverings.
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
add a comment |
A $(v,k,t)$ covering is a family of subsets of ${1,2,3dots v}$ such that each subset has $k$ elements and every subset of ${1,2,3dots,v}$ that has exactly $t$ elements is contained in one of the subsets of the family.
What you want to find is the minimal subsets that can be in a ${v,k,2}$ covering. Here is a repository of such coverings.
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
A $(v,k,t)$ covering is a family of subsets of ${1,2,3dots v}$ such that each subset has $k$ elements and every subset of ${1,2,3dots,v}$ that has exactly $t$ elements is contained in one of the subsets of the family.
What you want to find is the minimal subsets that can be in a ${v,k,2}$ covering. Here is a repository of such coverings.
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
answered Jan 3 '15 at 16:44
Jorge FernándezJorge Fernández
75.1k1190191
75.1k1190191
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
add a comment |
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Thank you!!! We're struggling in this problem for ages! I didn't know such a theory.
– Soft Cream
Jan 3 '15 at 16:55
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Yes, the case when $k=3$ has been much more extensively studied, The problem can be solve optimally when $v$ is congruent to $1$ or $3$ mod $6$ and it requires $frac{v(v-1)}{6}$ subsets. This is called a steiner triple system.
– Jorge Fernández
Jan 3 '15 at 17:12
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Thank you! Isn't there an explicit general expression for $A(v, k, 2)$?
– Soft Cream
Jan 3 '15 at 17:15
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
Please see this question
– Jorge Fernández
Jan 4 '15 at 17:42
add a comment |
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%2f1089811%2fphoto-booth-problem%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
