# Tagged Questions

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### Is the polar of the polar set the original set?

For each $Q \subset \Bbb R^n$, denote $Q^*:=\{z \in \Bbb R^n:z\cdot x \leq 1,\;\;\text{for all}\; x \in Q\}$. Let $P:=\{x \in \Bbb R^n: Ax \leq b\}$, for the matrix $A$ and the vector $b$. It is ...
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### on stochastic matrices

I have some questions on stochastic matrices in Discrete Mathematics as follows. The set $P_n$ of all $n \times n$ doubly stochastic matrices is a polytope in $\mathbb R^{n^2}$? If $A$ be a vertex ...
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### totally uni modular matrices with binary variables

I have this problem A*X<=B A is totally uni modular matrix, X is binary vector { 0 , 1} values . any help for finding polynomial algorithm for solving this problem?
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### Understanding the beginning, while, sum, and end of an algorithm

My problem is as follows: \1brace procedure sum (n: positive number) sum:=0 while i < 10 begin sum :=sum + i end output(sum) \rbrace Then, I have the following choices to select from as ...
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### Weak form for Linear Dynamic Wave Equation of Dirichlet/Neumann's boundaries?

I have a linear problem with double derivate of space and time, which has Dirichlet boundary condition in $(1)_{2}$ and Neumann's boundary condition in $(1)_{3}$: \frac{\delta^{2} ...
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### String satisfying the condition

Given $N$, $A_0$, $B_0$, $L_0$, $A_1$, $B_1$ and $L_1$, find a sequence S consisting only of characters '$0$' and '$1$'(a total of N characters) such that: The number of '$0$'s in any consecutive ...
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### Partial linear relaxation yields an integer solution

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
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### Find $n$ in $8n^2 \le 64n\lg n$

Given the solution. Can someone help me why $n \le 43$. What is the step by step of the solution for this?
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### Are there 0-1-matrices that are not unimodular?

I am just wondering if there are matrices that only consists of $0$s and a few $1$s that are not totally unimodular (TU)? I cannot come up with an example but I am not very experienced with this ...
Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...