# Tagged Questions

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### What is the number of sign patterns in $\frac n2$ of columns (or rows) of Hadamard matrices?

Given a Hadamard matrix of size $n$, I want to know what is the number of unique sign patterns in any $\frac n2$ columns (or rows). I count a sign pattern and its negation to be the same. My guess ...
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### permutations with a given condition!

What will be the number of permutations of n different things, taken r at a time,when p particular things is to be always included in each arrangement? I know the answer to this question but could not ...
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### Find value of $n$ with given conditions

The 4-digit positive number $n$'s digit sum is $20$. The sum of the first two digits is $11$, the sum of the first and the last digit as well. The first digit is the last digit $+3$. What is the ...
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### My fun conjecture about linearly independence

In the $\mathbb{R}^n$ vector space, there are distinct $m$ vectors $v_i$'s ($1< i\leq m)$ such that each component has value 0 or 1. Let $A_i$ be the set of $j$'s where $j$-th component of $v_i$ ...
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### solving recurrence relations for functions with more than one variable

Is there a way to find formula for a function on more than one variable which is given by recurrence relation with some initial conditions? e.g.if one knows the value of f(n,p,l) for all p,l where ...
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### How many are possibilities to build count $n$ summing $k$ other counts?

I have got an integer $n$. I have to build it by summing $k$, not necessary, different integers. Is there any overall formula to count how many are possibilities to build count $n$ summing $k$ other ...
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### Sum of $\mathbf{x}\mathbf{x}'\mathbf{x}\mathbf{x}'$ when $\mathbf{x}$ is a binary vector of length $n$

Let's say $\mathbf{x}$ is an $n\times 1$ column vector where each entry can be either 1 or -1. There can be $2^n$ possibilities for this vector. Let $\mathbf{x}'$ be a transpose of $\mathbf{x}$. I ...
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### Name search for special Linear Mixed Integer Programm

I am looking for a name for the following question in literature! (and if you know it, then it would be great) I couldn't find it and due to wide audience here, presumably you know more. Thank you ...
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### How many codimension 1 submodules of $(\mathbb{Z}/2)^n$ are there?

Let $\mathbb{Z}/2$ denote the ring of two elements. How many codimension-1 submodules of the $n$-dimensional free module $(\mathbb{Z}/2)^n$ are there?
Given a 0-1 matrix $A$, is there an efficient way to find all 0-1 vectors $x$ such that $Ax = v$ where the entries of $v$ belong to a set $\{a,b\} \subseteq \mathbb{Z}$ of size $2$? Note that $v$ is ...