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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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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Tverberg Partition
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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Recommended Book for Probability **OF A CERTAIN KIND** [closed]
There is this book titled "How to Prove it" by Daniel J. Velleman that introduces Discrete Mathematics in the absolute best way possible. If you've read it, you know EXACTLY what I'm talking ...
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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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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 ...
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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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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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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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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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