Vtyjkyuk

Clash Royale CLAN TAG #URR8PPP up vote 3 down vote favorite 1 Revisiting one of my older questions, I've decided to try to tackle a simpler version of the problem, this time without the square root coefficients. Let $x_0$ be a real number such that it satisfies the equation $$x_0+x_0^1/2+x_0^1/3+cdots+x_0^1/n=1$$ for a natural number $n$. What is the minimal polynomial in $mathbbZ[x]$? Of course, this is possible by brute force: isolating the smallest power of $x$ then raising both sides by its reciprocal and repeating, but it becomes extremely tedious to do when $n$ is large. Also, this does not guarantee that the polynomial obtained is minimal. This works fine for $n=1,2,3$. The minimal polynomials are, respectively, $$x-1,quad x^2-3x+1,quad x^5-8x^4+24x^3-21x^2+10x-1$$ and it may be interesting to note that the sign of the coefficients are alternating. Is there an efficient way of doing this for the general case? roots minimal-polynomials share | cite | impro...

Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite This coming academic year a professor has asked me to find some topics that I wish to pursue to write about. The problem/topic that will be discussed doesn't have to be open, but my trouble is that I need ideas for topics in the first place. Can anyone suggest research topics dealing with preferably Combinatorics? It is my favorite subject so far since I haven't delved into Graph Theory too much. combinatorics graph-theory open-problem share | cite | improve this question asked Jul 10 '14 at 4:16 Ozera 1,037 4 15 31 1 Douglas West and Dan Archdeacon both maintain lists of open problems on their websites, which I will link to below. I would say nearly any of the problems could be understood by a motivated undergrad. Most of these are graph theory problems, but there are several purely combinatorial problems there too. math.uiuc.edu/~west/openp emba.uvm.edu/~darchdea/p...