Tagged Questions

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Theoretical computer science text for mathematician

I am a high school student, I know some basic programming in java,python and visual basic. I love combinatorics and I have encountered various cases in which I have found some problems are really ...
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How do you find a minimum of a function with these tools?

Let's say I can define a group $G$ acting on a set of combinatorial objects $X$ and I have a function $f: X \to \Bbb{N}$ that I want to find a minimum of in $X$. Is there a polynomial time ...
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Application of Combinatorics, Logic and computability theory in physical science: Tiling of Wang Tile with proportionality

The original problem of Domino Tiling and Wang Tile has great theoretical interest on computability theory... However, the great emerging problem on application of Wang Tile in material science and ...
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The complexity of counting solutions to $x_1 + \dots + x_m = N$ in non-negative integers under constraints

Consider the equation $$x_1 + \dots + x_m = N$$ where $x_1,\dots,x_m \ge 0$ and under the additional constraints $x_k \le a_k$ for $k=1,2,\dots,m$. I'm interested in knowing whether the number of ...
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Why is Dantzig's solution to the knapsack problem only approximate

For a bunch of items with values $v_i$ and weights $w_i$, and with a total weight $W$ that our bag can carry, how do we achieve maximum total value without breaking the bag? Dantzig proposed that we ...
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The $k$-th term in the graded lexicographical order is recursive

I recently constructed a proof that a computable universal function exists for the class of polynomials of $n$-variables. To this end, I adopted the graded lexicographical monomial order. However, I ...
In short: In how many ways can all $2^n$ subset sums of $n$ real numbers $a_1,\ldots, a_n$ be ordered? I am not concerned about the case in which different subsets sum to the same number; you may ...