# Tagged Questions

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### Counting the number of elements in a double coset

Let $G$ denote the groups of $n\times n$ invertible matrices and $H$ be the subgroup of invertible upper triangular matrices. For $n=2$, by row reduction, or equivalently LU decomposition, it is ...
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### The Number of Increasing Vectors $(x_1,…,x_k)$ Satisfying $1 \leq x_i \leq n$ and $x_1 < x_2 <…<x_k$

I want to find the number of increasing vectors $(x_1,...,x_k)$ satisfying $1 \leq x_i \leq n$ and $x_1 < x_2 <...<x_k$. Examples of vectors satisfying these conditions Let $n =5$ and ...
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### Is there a binary [10,6,4] code?

Using the sphere padding packing bound formula I can conclude that 1 + 12 + 66 $\ge$ $2^{6}$ which indicates that there MAY be a binary [10,6,4] code, however I cannot prove that there is. How can I ...
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### Finding maximum no of $1$'s

We are given a matrix $A \in M_n (F)$ such that all its entires are either $1$ or $0$. I need to find the maximum number of $1$'s that can be in matrix $A$ so that it is still invertible. My try : ...
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### Prove that the minimum of row sums of a nonnegative symmetric matrix is preserved

Let $A$ be an $n\times n$ adjacency (nonnegative, irreducible and symmetric) matrix with zeros on the diagonal. Denote $i$-th row sum of $A^k$ as $r^{(k)}_i$, where $k\geq1$. I want to prove that if ...
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### psittacism: Fundamental Theory of Time

This question is in reference to the programming question found here. What method of approach should I be thinking of if I have a list of lectures A, B, and C, and discussions D, E, and F, that are ...
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### How to tell if two matrices are equal up to a permutation

Given two real rectangular matrices A, B how can I tell if they are equal up to a permutation of their rows/column without trying all possible permutations? (This is closely related to the question I ...
I expect this is elementary, but I can't find a closed form. Let $a_i$, $i=1,...,m$, be a sequence of natural numbers and $n>\sum a_i$. What is the value of the sum: ...