(Copiedfrom MSE. Offering four bounties over time, I got no response, other than twenty-nine upvotes.)

It seems preposterous at first glance. I just want to be sure. ...

Let denote the unit ball on and be the cardinality of the smallest -cover of . An epsilon cover is a set such that for any , there is a with . See for example [here](https://www.stat.berkeley.ed...

Let be the all-ones vector, and suppose are mutually orthogonal non-zero vectors. Does it follow that ?

A few notes are in order:

1. If we do not a...

Let , for some finite set of points, say with . The category of locally constant sheaves of -vector spaces on (equivalently, complex representations of ), , has many natural autoequivalences.

For examp...

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal.

More precisely, given a set of 1 and 2 qubit gates, can we write a program to determine whether this constitutes a universal gate set? If so, how might we do this?

EDIT: To clarify ...

In this question, it was asked wether a MIP formulation exists to test for a graph's planarity. The inputs are the graph's nodes and edges, and the output would be a certificate which guarantees tha...

I tried to vectorize the premultiplication of 64-bit colors of 16-bit integer ARGB channels.

I quickly realized that due to lack of accelerated integer division support I need to convert my values to float and use some SSE2/SSE4.1 intrinsics explicitly for the best performance. Still, I wanted to...

I am currently migrating from xltabular to tabularray. As part of that I want to adapt my custom glossary style for List of Symbols and List of Abbreviations (same style).

This is my old code:

% tables
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{xltabular}
...

For an element of a group and an irreducible character, there are two easy bounds for the character value : First, the bound by the dimension of the representation and, second, the bound by the centralizer arising from the...

Consider a prime number and denotes the remainder of upon division by . Let .

I Conjecture

The question has already been asked in this [thread](https://math.stackexch...

Does there exist a function , holomorphic on the whole complex plane , such that and ? If yes, is it possible to have an explicit construction? Note that, for example, $h(z)=...

Non-overlapping circles of radius are all externally tangent to a middle circle.

How should we arrange the surrounding circles, in order to minimize the middle circle's radius ?

Take for example.

On the left, going anticlockwise the radii are $1, 2, 3, 4, 5, 6, 7, 8, 9...

What functions from can be made from , , , , exponentiation, and ? Call this class of functions (for "floor and exponentiation"). The function can be defined by . In add...

Within IBM's internal Development community, there was a move in the 1980s to bring our skills up to date. As part of this, we were introduced to a specification language, independent of the programming languages of the time (PL/S and Basic Assembler for example), in which a specification would be i...

Calculate the limit

or prove that the limit does not exist. This appeared as a problem in my mathematical analysis test, and the answer was that the limit exists and it was . But later the teacher found a mistake in his proof and eventually remove...

In eusocial animals for which hearing is important to communicate between individuals, is there any species apart humans for which there are some evidence that the group adapts their acoustic communication to a fully or partially deaf individual of the group?

For instance, by systematically vocaliz...

_This is a tweaked version of a question which was asked and bountied[at MSE](https://math.stackexchange.com/q/4555946/281...

I have a vague recollection of this book, mostly the X-shaped alien. I can’t find anything through internet searches. I thought it may be some sort of “choose your adventure” book, but I haven’t seen it on any lists or pages discussing those sorts of books.

Alien description:

• Hugging a water w...

The infinite dihedral group is a finitely generated group with infinitely many cyclic subgroups of order 2, every one of which is a retract.

For the group ‎, ‎take for any integer ...

Let be a number field, a finite set of places, and a smooth projective -scheme with geometrically connected fibers. For each point , there is a Chern class map where denotes a...