# Tagged Questions

**8**

votes

**0**answers

411 views

### Reference/quote request: “All of combinatorics is the representation theory of $S_n$”

I think I remember reading somewhere a glib (or is it deep?) quote, perhaps due to Rota?, which was something like
"All of combinatorics is essentially [or can be reduced to?] the representation ...

**3**

votes

**0**answers

121 views

### Citation for subset complement result

Let $S=\lbrace s_1,\ldots,s_n \rbrace \subset \lbrace1,\ldots,2n\rbrace$. Consider two operations on $S$: the complement $C(S)=\lbrace 1,\ldots,2n \rbrace \setminus S$ and a reflection* ...

**6**

votes

**3**answers

650 views

### Classification of Platonic solids

My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula ...

**5**

votes

**1**answer

221 views

### constant averages along orbits

What should one say to describe the situation in which a function $T$ from some set $X$ to itself, and a function $f$ from $X$ to some characteristic-zero field $K$, have the property that the average ...

**3**

votes

**1**answer

184 views

### Historical question about MacMahon theorem, Wronski relation etc…

Seemingly the same fact goes under several names: MacMahon master theorem, Wronski relation, unnamed fact about symmetric functions - I wonder what is history and what should be ``correct name'' ?
...

**13**

votes

**0**answers

840 views

### Origins of the Nerve Theorem

Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question:
Who was the first to prove the Nerve Theorem?

**3**

votes

**1**answer

408 views

### Klein Bottle exception to the Heawood Conjecture [duplicate]

Possible Duplicate:
The Klein bottle and the Heawood Conjecture
It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a ...

**7**

votes

**3**answers

778 views

### What is so “plactic” about the plactic monoid?

The plactic monoid is the monoid consisting of all words from the alphabet $\mathbb{Z}^+$ modulo certain relations. It is important mainly because its elements enumerate semistandard Young tableaux.
...

**5**

votes

**1**answer

448 views

### Where does the definition of “Tower of Algebras” come from?

A tower of algebras is a sequence of algebras
$$A_0 \hookrightarrow A_1 \hookrightarrow \cdots \hookrightarrow A_n \hookrightarrow \cdots$$
with embeddings $A_n \otimes A_m \hookrightarrow A_{n+m}$ ...

**19**

votes

**1**answer

1k views

### Fibonacci, compositions, history

There are three basic families of restricted compositions (ordered partitions) that are enumerated by the Fibonacci numbers (with offsets):
a) compositions with parts from {1,2}
(e.g., 2+2 = 2+1+1 = ...

**4**

votes

**3**answers

958 views

### Why were plane partitions invented?

I realize that these objects were originally created by Major Percy Macmahon and today have many applications but what was the original motivation for studying them?

**7**

votes

**9**answers

430 views

### What are some early examples of creation of lists / catalogues of (particularly) combinatorial objects?

A lot of effort in discrete maths / combinatorics is expended in the construction of lists, catalogues or census [sic] of combinatorial objects such as groups, graphs, designs etc. These catalogues ...

**3**

votes

**2**answers

755 views

### Birkhoff's theorem about doubly stochastic matrices

Birkhoff's theorem states:
The set of $n \times n$ doubly stochastic matrices is a convex set whose extreme points are the permutation matrices
This theorem seems to be commonly attributed to ...

**24**

votes

**3**answers

1k views

### Does there exist a comprehensive compilation of Erdos's open problems?

Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single ...

**29**

votes

**4**answers

6k views

### Do actual Sudoku puzzles have a unique rational solution?

Here is a question in the intersection of mathematics and sociology. There is a standard way to encode a Sudoku puzzle as an integer programming problem. The problem has a 0-1-valued variable ...

**17**

votes

**4**answers

2k views

### Genealogy of the Lagrange inversion theorem

A wonderful piece of classic mathematics, well-known especially to combinatorialists and to complex analysis people, and that, in my opinion, deserves more popularity even in elementary mathematics, ...

**7**

votes

**5**answers

1k views

### Texts on the General History of Contemporary Combinatorics

I am looking for some core texts (books, book chapters, papers) about the general history of contemporary combinatorics, starting, say, from the interwar period up to today.
Texts about the history ...