Lv 31,259 points

# Gabriel D

When I answer a question I try to answer as fully as possible because I want others to do the same for me. An answer is not helpful, especially in math, without an explanation of how you got it. I also tend to answer problems I am very comfortable with, mainly basic algebra through basic calculus. People need to be more specific in what their math question is about-don't say just math problem- say what class it's for and what type it is. If you ask a question and get a good answer or two, give someone the credit of getting the 10 points for best answer-it's a way of saying thank you. About me: I'm just a student at the Ohio State University looking to get a math minor and a degree in middle childhood education with a focus in math and science. I love to help people understand things and that is why I want to teach. I am thankful for the knowledgeable people at YA that continually help me to get through the rough math I don't understand

• ### What is the total number of knights moves on an mxn chessboard?

What is the total number of knights moves on an mxn chessboard?

I don't know how to find an algorithm for that and this is one of the problems in my homework. Any help would be appreciated-thanks!

• ### Combinatorics-proof of trees.?

Prove that a graph is a tree if and only if it doesn't have any cycles, but adding another edge always creates exactly one cycle.

NOTE: I can visually understand what it's saying but I don't know how to put it into a proof format. I mean, a graph that is a tree is taking the shortest route possible, with each vertex being connected to one other vertex. But if another edge is added in it must connect two vertices that are part of the graph and already have at least one edge connecting them to another vertex in the graph. And that vertex is connected to another and so on for all the vertices, making it a cycle. Now how do I say all that legitimately in a mathematical proof...I have no idea.

• ### Combinatorics-tree problem?

Let G be a forest of K trees. What is the fewest number of edges that can be inserted in G to obtain a tree?

Is it simply K-1, because K things can be connected by a minimum of K-1 edges? Or is that not right, and it's more complex?

Thanks.

• ### Combinatorics-forbidden squares on chessboard problem?

Consider an n-by-n chessboard with forbidden positions for which there exists a positive integer p such that each row and each column contains exactly p allowed squares. Prove that is is possible to place n nonattacking rooks on the board.

Thanks.

• ### Combinatorics-graph theory problem.?

Prove that any two multigraphs G of order 3 with degree sequence (4,4,4) are isomorphic. Then:

a) determine all the nonisomorphic induced subgraphs of G

b) determine all the nonisomorphic spanning subgraphs of G

c) determine all the nonisomorphic subgraphs of order 3 of G

Our professor in Combinatorics did not go over induced subgraphs and spanning subgraphs, so I have no idea what either of them are. Basically, the professor I have is a really bad teacher.

Please explain as fully as possible. Thanks.

• ### Combinatorics-proof of edges being connected.?

Prove that a graph of order n with at least ((n-1)(n-2))/2+1 edges must be connected. Give an example of a disconnected graph of order n with one fewer edge.

Please include a detailed explanation. Thanks. And if you know how to do this, you may know how to answer a couple more of my unanswered questions. Just look on my profile to find them.

• ### Combinatorics-Systems of Distinct Representatives proof problem?

Let n>1 and let Ą=(A1, A2,...,An) be the family of subsets of a {1,2,...n}, where Ai={1,2,...,n} - {i}, (i=1,2,...,n).

Prove that Ą has an SDR (system of distinct representatives) and that the number of SDR's is the nth derangement number Dn.

Any help on this problem would be appreciated. Please answer as completely as you can so I can hopefully understand what's going on. Thanks.

• ### Combinatorical proof relating to basic graph theory.?

Prove that any two connected graphs of order n with degree sequence (2,2,...,2) are isomorphic.

Thanks.

• ### Combinatorics-bipartite graph problem maximum?

Here it is:

A business has 7 available positions y1,y2,...,y7 and 10 applicants x1,x2,x3,...,x10. The set of positions of each applicant is qualified for for is given, respectively by {y1,y2,y6}, {y2,y6,y7}, {y3,y4}, {y1,y5}, {y6,y7}, {y3}, {y2,y3}, {y1,y3}, {y1}, {y5}. Determine the largest number of positions that can be filled by the qualified applicants and justify your answer.

Now-I know that I need to make a bipartite graph with the x's and y's, which I did. Now I have a bunch of lines. I know the idea is to find a way to reach Breakthrough. But, looking at my combinatorics book, it doesn't explain it well enough. The graph with and without breakthrough look pretty much the same. So I don't what breakthrough is and thus I can't do it for this problem. Any help with that, relating to this problem would help. I can see it as very hard trying to make a bipartite graph and putting it on here, so you don't have to do that unless you want to. But an explanation of how to do the problem would be nice.

Thanks for the time.

• ### Combinatorics-chessboard forbidden positions problem.?

Here's the problem:

Think about a chessboard that has forbidden positions which has the property that, if a square is forbidden, so is every square below it and to its right. Prove that the chessboard has a perfect cover by dominoes IF AND ONLY IF the number of allowable white squares equals the number of allowable black squares.

Now I have figured out that if make a chessboard, that if you move one up and to the right every time, you will have basically stair steps on the chessboard. Half the board forbidden and half not. But I don't know if this helps or where to go from there.

Please answer as fully as possible so I can understand the problem after reading or seeing the explanation. Thank you.

• ### Combinatorics problem- basic graph theroy?

Let (d1, d2,....,dn) be a sequence of n nonnegative integers whose sum d1+d2+...+dn is even. Prove that there exists a general graph with this sequence as it's degree sequence. Find an algorithm to make such a general graph.

I don't know how to do this. Please answer as completely as possible. Thank you for your time.

• ### Combinatorics question- bipartite graph problem?

Let G=(X, ∆, Y) be a bipartite graph. Suppose there is a integer p in the positive integers such that each vertex in X meets at least p edges, and each vertex in Y meets at most p edges. By counting the total number of edges in G, prove that Y has at least as many vertices as X.

Well, wouldn't the total edges be p because each X connects to at least one Y each Y connects to at least one X? If that is even right, how do I prove the vertices?

• ### Combinatoric problem- derangement with additional rule.?

Find the number of permutations of the multiset S={3*a,4*b,2*c} where for each type of letter, the letters of the same type don't show up consecutively (abbbbacac is not allowed, but abbbacacb is}

Please answer the question the fullest you can so I can learn to do this myself. Thanks for the time and answers.

• ### Combinatorics question dealing with derangements.?

Dn is the derangement. I need to show that n!= (n choose 0)Dn + (n choose 1) Dn-1 + (n choose 2) Dn-2+...+(n choose n-1)D1 + (n choose n)D0 by combinatorial reasoning.

Thanks.

• ### Need combinatorics help with derrangement question?

The question is this: Determine the number of permutations of {1,2,....,8} in which no even integer is in it's natural position.

I don't know how to do this. I have the answer though, but that is not enough. I need to know how to do this. If you can help me, please do. Thanks!

• ### Anyone know how to purchase songs on grooveshark?

I love listening to music on Grooveshark and I know that they say you can purchase songs, but the website is very hard to navigate and I can't find out where to buy them. Any help? Is it disabled right now? A link to where to buy the music if it's active would be nice. Please, don't point me to another site, I can find one myself all I want to know how to do it on Grooveshark.

• ### How to turn an automatic option of Spybot-search and destroy?

It has come to my attention that after downloading the new version of Spybot search and destroy that when I try to open any of my .avi extension files (basically it is a movie format) by double clicking on the file instead of opening it like I want it to, it automatically scans the file with Spybot. This is true for all of my .avi files. I've told it to open in windows media player when I double click on it, but it's set in stone to scan it with Spybot. I can open it, however, by opening media player and then opening the file. I want to know how to get rid of that option on Spybot because it's really starting to annoy me. I've already looked at the help and FAQ and I can't find anything. Please help.

• ### Combinatorics problem dealing with clutters. HELP!?

Prove that there are only 2 clutters of S={1,2,3,4,5} of size 10 namely the clutter of 2 combinations and the clutter of 3 combinations of S.

Now I know that (n-1)/2 and (n+1)/2 are the two combinations that are of size 10 by Spencer's theorem (for the odd numbered element sets), that would make them (5-1)/2 and (5+1)/2= 2 and 3. I feel like that is not enough though. I would appreciate any help. Thanks.

• ### Combinatorics proof:?

Prove that for all real numbers r and all integers k and m: (r choose m)*(m choose k)=(r choose k)*(r-k choose m-k). Thanks for your time. Also, if you do this one consider trying this one for me too: