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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Column/Digit blind solution for the "Number of possible combinations of x numbers that sum to y"
What formula will give me "the total number of possible combinations of x digits that sum to y".
This is a branch question from the original question entitled
Number of possible ...
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1
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Regarding the question of translating the verbal descriptions of definitions and theorems into propositional logic
I am studying discrete mathematics and recently trying to describe mathematical definitions or theorems in the form of propositional calculus or predicate calculus. I am not sure if my approach is ...
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Number of Tverberg Partitions
Tverberg's Theorem: A collection of $(d+1)(r-1) +1$ points in $\mathbb{R}^d$ can always be partitioned into $r$ parts whose convex hulls intersect.
For example, $d=2$, $r=3$, 7 points:
Let $p_1, p_2,...
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Helly's theorem for $n\geq d+3$
Helly's theorem : Let $C_1,\ldots,C_n$, $n\geq d+1$, be convex sets in $\Bbb R^d$. Suppose every $d+1$ have a common intersection. Then they all have a common intersection.
Proof: We're given that ...
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Steps on solving part b of the bit-string exercise?
This is the exercise:
How many bit strings of length $77$ are there such that
a.) the bit
string has at least forty-six $0$s and at least twenty-nine $1$s, and also
the bit string corresponding to ...
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0
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26
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Construction of a graph on even number of vertices with required eccentricities.
I was trying to construct a graph on an even number of vertices $n$ such that center and periphery contain an equal number of vertices, i.e. $|C(G)|=|P(G)| =\frac{n}{2}$. Till now, I was able to draw ...
- 4,470
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Is the law of non-contradiction part of formal mathematics?
I am seeking hereby to clarify whether the law of non-contradiction is part of the framework in which mathematicians work or not. Wikipedia says only that this is a principle in "logic", ...
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The number of ways of writing $k$ as a sum of the squares of "not so big" two elements
This question arises from the attempt to compute the Euler characteristic
of a space using a Morse function.
We fix a positive integer $n$. For each integer $k$ which satisfies the condition
$$1\leq k ...
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2
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51
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Sequences of cyling digits [closed]
Have been wrestling with this one: Given five policy numbers (rows of integers like on an insurance policy). The 2nd is 2X the first when the first #'s one's digit is moved to its front; similarly for ...
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What is the number of facets of a $d$-dimensional cyclic polytope?
A face of a convex polytope $P$ is defined as
$P$ itself, or
a subset of $P$ of the form $P\cap h$, where $h$ is a hyperplane such that $P$ is fully contained in one of the closed half-spaces ...
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Confused about a counting problem
This question is reproduced from a text by Sheldon Ross:
Example 5k. A football team consists of $20$ offensive and $20$ defensive players. The players are to be paired in groups of $2$ for the ...
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1
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Does any permutation "cover" a permutation with less inversions?
Let $\mathcal{S}_n$ be the symmetric group on $n$ objects. For any permutation $\pi\in\mathcal{S}_n$, define $E(\pi)=\{(i,j):\ i<j,\ \pi(i)>\pi(j)\}$ as the set of reversed pair of indices ...
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I dont understand how to solve this Boolean Algebra question Help
Let S be a set and let F UN(S, {0, 1}) be the set of all functions with domain S
and codomain {0, 1}. Define the Boolean operations on F UN(S, {0, 1}) as follows:
Let F, G ∈ F UN(S, {0, 1}), then
(a) ...
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0
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Removing vertices from rooted tree to make it balanced
The question says, what is the least number of vertices that must be deleted from T to yield a balanced tree. The correct answer is 1. But how, i see the graph is already balanced and doesn’t need ...
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Probability that at least one option is selected exactly once [closed]
I'm having trouble with the following question: Suppose $n$ persons each select, uniformly and independently, one of $k$ options. Show that the probability that at least one option is chosen exactly ...
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