All Questions
40
questions
4
votes
1
answer
149
views
FLT (Fermat): Combinatorial approaches?
Such a simple equation like $x^n+y^n=z^n$ is bound to have a nice/natural combinatorial interpretation. One very crude one is: Let the number of ways of choosing $n$ objects from $x$ objective, ...
- 2,242
1
vote
2
answers
89
views
Does this function have closed form?
Define $$f(p,n)=\sum_1^n s_i$$ where $s_i$ is defined as the maximal integer value such that $i= p^{s_i}r_i$ for integer $r_i$.
For example, we'd have $$f(2,15)=\sum_1^{15} s_i=1+2+1+3+1+2+1=11.$$
...
- 1,113
2
votes
0
answers
152
views
Game theoretical approach to other branches of mathematics
Are there some methods and ideas derived from game theory that are successfully applied to better (or more intuitively) understand theorems and proofs or tackling problems from other areas of ...
- 8,294
1
vote
0
answers
53
views
Ehrhart Polynomials Modulo Prime Integers
Are there any results known about computing Ehrhart Polynomials modulo prime integers?
- 1,300
3
votes
0
answers
144
views
Generalization of small set/large set
A small set is a subset of the positive integers, such that the infinite sum of the reciprocals of the members of the set converges. Conversely, the sum of the reciprocals of a large set diverges.
...
- 3,199
7
votes
1
answer
175
views
Gowers' proof of Szemerdi's theorem
Are there any good books or other resources (expository notes) which explains Gowers' proof of Szemerdi's theorem in detail?
- 15.1k
1
vote
2
answers
147
views
Does there exist a branch of mathematics that specifically study the number of lattices enclosed by a region?
I have seen that sometimes, in particular in number theory and combinatorial commutative algebra, our questions are somehow related to finding the number of points with integer components in a region/...
- 7,399
1
vote
1
answer
137
views
generalization of base-n notation from naturals to fractions
not exactly sure how to best ask this. base-$n$ notation involves a series of digits written where each digit is a natural number less than $n$.
is there some math/theory generalization of base-$n$...
- 844
5
votes
1
answer
460
views
Arithmetic progressions
What are the largest known lower bounds for $B_k$, the maximal sum of the reciprocals of the members of subsets of the positive integers which contain no arithmetic progressions of length $k$?
for $k=...
- 53
7
votes
1
answer
398
views
"On the consequences of an exact de Bruijn Function", or "If Ramanujan had more time..."
In this question on Math.SE, I asked about Ramanujan's (ridiculously close) approximation for counting the number of 3-smooth integers less than or equal to a given positive integer $N$, namely,
\...
- 17.1k