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Questions tagged [discrete-mathematics]

Questions about discrete mathematics, the study of mathematical structures that are fundamentally discrete rather than continuous.

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

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What use are groups, monoids, and rings in database computations?

Why would a company like Twitter be interested in algebraic concepts like groups, monoids and rings? See their repository at github:twitter/algebird. All I could find is: Implementations of Monoids for interesting approximation algorithms, such…
john mangual
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Counting binary trees

(I'm a student with some mathematical background and I'd like to know how to count the number of a specific kind of binary trees.) Looking at Wikipedia page for Binary Trees, I've noticed this assertion that the number of rooted binary trees of size…
Stéphane Gimenez
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Pizza commercial claim of 34 million combinations

A pizza commercial claims that you can combine their ingredients to 34 million different combinations. I didn't believe it, so I dusted off my rusty combinatorics skills and tried to figure it out. Here's what I have so far: From the online…
gebuh
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How hard is finding the discrete logarithm?

The discrete logarithm is the same as finding $b$ in $a^b=c \bmod N$, given $a$, $c$, and $N$. I wonder what complexity groups (e.g. for classical and quantum computers) this is in, and what approaches (i.e. algorithms) are the best for…
Matt Groff
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What is an intuitive way to explain and understand De Morgan's Law?

De Morgan's Law is often introduced in an introductory mathematics for computer science course, and I often see it as a way to turn statements from AND to OR by negating terms. Is there a more intuitive explanation for why this works rather than…
Ken Li
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Real life examples of negative weight edges in graphs

I am unable to relate to any real life examples of negative weight edges in graphs. Distances between cities cannot be negative. Time taken to travel from one point to another cannot be negative. Data transfer rates cannot be negative. I am just…
Sandeep
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Why is Integer Linear Programming in NP?

The decision version of the problem Integar Linear Programming is the following: Input: two matrices $A\in \mathcal{M}_n(\mathbb{Z})$ and $B\in \mathcal{M}_{n,1}(\mathbb{Z})$. Question: is there a matrix $X\in \mathcal{M}_{n,1}(\mathbb{Z})$ such…
Nathaniel
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On "The Average Height of Planted Plane Trees" by Knuth, de Bruijn and Rice (1972)

I am trying to derive the classic paper in the title only by elementary means (no generating functions, no complex analysis, no Fourier analysis) although with much less precision. In short, I "only" want to prove that the average height $h_n$ of a…
Christian Rinderknecht
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Polytime and polyspace algorithm for determining the leading intersection of n discrete monotonic functions

Some frontmatter: I'm a recreational computer scientist and employed software engineer. So, pardon if this prompt seems somewhat out of left field -- I routinely play with mathematical simulcra and open problems when I have nothing better to do.…
MrGomez
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Bridge theorems for group theory and formal languages

Is there some natural or notable way to relate or link math groups and CS formal languages or some other core CS concept e.g. Turing machines? I am looking for references/applications. However note that I am aware of the link between semigroups…
vzn
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How to practically construct regular expander graphs?

I need to construct d-regular expander graph for some small fixed d (like 3 or 4) of n vertices. What is the easiest method to do this in practice? Constructing a random d-regular graph, which is proven to be a.a.s. an expander? I also read about…
user2145167
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Fast algorithm for max-convolution with concave functions?

I'm interested in a discrete max-convolution problem, which is to compute $$r(c) = \max_{x | x \ge 0, \sum_k x_k = c} \left[ \sum_{k=1} f_k(x_k) \right] $$ for all values $c=0, \ldots, C$, where $x=(x_1, \ldots, x_k)$ is a vector of non-negative…
dan_x
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Why is the minimum height of a binary tree $\log_2(n+1) - 1$?

In my Java class, we are learning about complexity of different types of collections. Soon we will be discussing binary trees, which I have been reading up on. The book states that the minimum height of a binary tree is $\log_2(n+1) - 1$, but…
CodyBugstein
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How to construct this generalized xor without needing an extra vector?

Operator - Generalized Symmetric Difference If you take binary xor and generalize it to other radices you can do so by the absolute value of the difference of each element in a radix vector. However this doesn't have the same properties as the…
Cris Stringfellow
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Problem of constructing binary sequence with least possible 1s under given constraint

You are given a binary pattern p. Problem is to construct a binary sequence of length n such that by sliding p over our sequence there is always at least one position where two 1s align (one in the pattern and other in our sequence). The goal is to…
Relja Šegvić
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