Edit: question has been changed from 'lexicographic' (cf. "D K"'s answer below) to 'degree' minimality. Let $x_1,x_2,x_3$ be indeterminates. Fix an integer $k> 3$. Consider the se …

This problem appear in my research, but I am unable to solve it. There should be an easy argument, but I have not yet found it. Informal version An integer $k\geq 2$ is fixed. We …

I'd like to start by noting that for some fixed natural $N$ basis functions for my system will be generated by $f(k,x)$ as defined and explained here or in numerous other sources: …

Hi all, I have a cube, sized 39 x 13 x 8. I need to find out how many of them can fit in a cube of 100 x 100 x 100. I need to find the highest number possible. Do you know of a w …

Hello, I have the following two variable recurrence equation for integers $j,k$: $f(j,k) = (k/j)f(j-1,k-1) - (3 + k/j)f(j-1,k+2)$ where $f(j,0) = (3^j - 1)/j + 3jf(j-1,2)$, $f(0 …

Hello members, let's consider the following equation $$X=F_{1}XF_{1}^{T}+...+F_{p}XF_{p}^{T}+C$$ where $p$ is an positive integer and $C$ is a known positive semidefinite matrix. I …

Here I describe the sort of reference I'm after with a motivating example. I am not seeking solutions to my equations on this forum; I'm quite happy to do that myself. Rather, I'm …

Hello, members. I have a problem for the following problem when I derive an optimization algorithm for stochastic singular systems $$S(k+1)=A(k)S(k)A^{T}(k)+R(k)+F(k)S(k+1)F^{T}( …

Can anybody help me in finding out the distances between vertices in a vertex transitive graphs. Is there any specific formula to calculate distance between vertices in this graph. …

It is a famous result of Aldous and Diaconis1 that seven shuffles are necessary and suffice to approximately randomize 52 cards.2 Here the shuffles are the standard riffl …

Let $S=\lbrace s_1,\ldots,s_n \rbrace \subset \lbrace1,\ldots,2n\rbrace$. Consider two operations on $S$: the complement $C(S)=\lbrace 1,\ldots,2n \rbrace \setminus S$ and a reflec …

Let $X$ be a finite set of $n$ elements, and consider a binary operation $\odot: X \times X \rightarrow X$. There are $n^{n^2}$ such binary operations, as the $n \times n$ table e …

I recently stumbled upon the Mathieu groupoid and I found them fascinating. It appears as a subset of $S_{13}$ which is not closed under multiplication, but it turns out to be a g …

Regarding this question: http://mathoverflow.net/questions/72668/how-to-compute-kl-divergence-when-pmf-contains-0s One of the solutions requires the use of a "Dirichlet Prior", I …

Among the many upper bounds for families of codes in $\mathbb F _2 ^n$, the best known bound is the one by McEliece, Rodemich, Rumsey and Welch which states that the rate $R(\delta …