# Questions tagged [discrete-mathematics]

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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### Minimal time gossip problem

The gossip problem (telephone problem) is an information dissemination problem where each of $n$ nodes of a communication network has a unique piece of information that must be transmitted to all the ...
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### Counting the labellings of paths in perfect binary trees

Suppose that we have a set of $n$ labels $L = \{\ell_1, \ell_2, \ldots, \ell_n\}$ and a perfect rooted binary tree $T$ of height $r \leq n$. For my purpose, the tree containing a single node will be ...
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### Maximal Hamming distance

Here is a combinatorial problem: let $\Sigma=\{\alpha_1,\ldots,\alpha_n\}$ be an alphabet and we consider any words over $\Sigma$ of length $n$. We also define over the set of such words the Hamming ...
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### Using discrete calculus to study convergence of series and sequences

From some personal investigation, I've noticed that all convergence tests for infinite series (at least, the real kind) can be rephrased in terms of the discrete derivative $∆f(x)$ of a function $f(x)$...
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### Upper bounds on rate of q-ary codes

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 (MRRW) which states that the rate $R(\delta)$ ...
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### Prove that $(A\setminus B)\cup (B \setminus A)\subseteq (A\cup B)\setminus(A\cap B)$

I am asked to prove that $$(A\setminus B)\cup (B\setminus A)\subseteq (A\cup B)\setminus(A\cap B)$$ where $A$ and $B$ are sets. Could someone please check my solution and see if it is correct? I ...
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### Longest path through chessboard of arbitrary size

The original problem: You have a $8\times 6$ board. Your task is to color some tiles white and some black. There must be a unique beginning and end of the white trail and only one way to get from one ...
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### Small & Balanced family of sets

I have the following problem: Let $\epsilon >0$, and $[n] = \{ 1,2,...,n\}$ the set of positive integers up to $n$. There exists a family of subsets $\mathcal{F} \subseteq 2^{[n]}$, such that ...