Questions tagged [conjectures]
for question related to conjectures.
212 questions
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A conjecture about certain values of the Fabius function
The Fabius function is a smooth monotone function $F:[0,1]\to[0,1]$, satisfying functional equations
$$F(0)=0, \quad F(1-x)=1-F(x)\tag1$$
and
$$F'(x) = 2 \,F(2 x) \quad \text{for} \,\, 0<x<1/2.\...
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Why is $\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $?
This question is an old question from mathstackexchange.
Let $f_- (n) = \Pi_{i=0}^n ( \sin(i) - \frac{5}{4}) $
And let
$ f_+(m) = \Pi_{i=0}^m ( \sin(i) + \frac{5}{4} ) $
It appears that we have
$$\sup ...
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A constant bizarrely related to the Fibonacci Numbers
For roughly the past month, I have been studying denesting radicals. For example: the expression $\sqrt[3]{\sqrt[3]2-1}$ is a radical expression that contains another radical expression, so this ...
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A counterexample to a conjecture of Lawson
Yau quotes Lawson as having formulated the following conjecture [1]:
Let $M$ be an embedded minimal surface in $\mathbf{S}^3$. Prove that the two domains in $\mathbf{S}^3$ divided by $M$ have equal ...
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Does the interior of Pascal's triangle contain three consecutive integers?
This question defeated Math SE, so I am posting it here.
Consider the interior of Pascal's triangle: the triangle without numbers of the form $\binom{n}{0},\binom{n}{1},\binom{n}{n-1},\binom{n}{n}$.
...
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Is the conjecture A+B=C following correct?
Is the conjecture on A+B=C following correct ?
Conjecture: Let $A, B, C$ be three positive integer numbers such that $A+B=C$ with $\gcd(A, B, C) = 1$. By Fundamental theorem of arithmetic we write:
$...
- 1,776
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A conjecture of Blakley and Dixon about odd powers of positive matrices
In a 1966 paper Blakley and Dixon conjecture the following. Let $S$ be a symmetric matrix with nonnegative entries and let $u$ be a unit vector with nonnegative entries. For integers $k\ge j$ both odd,...
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Isoperimetric inequality, isodiametric inequality, hyperplane conjecture... what are the inequalities of this kind known or conjectured?
I duplicate here a question I asked on math.stackexchange.
Question: Which inequalities similar to the famous isoperimetric inequality is known?
conjectured?
I recently learned about some ...
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Almost Complex Structures: 'Tame' versus 'Compatible'
Consider a symplectic manifold $(M,\omega)$ and the space of almost complex structures. These are $J:TM\to TM$ with $J^2=-\text{id}$. A given $J$ is $\omega$-tame when $\omega(v,Jv)>0$, and $J$ is $...
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$π(x+y) - π(x) ≤ c·y/\ln(y)$ for some constant $c$?
(I posted this question on Math SE but it has had no answer for a year now so I would like to ask if anyone here can provide one.)
Thinking about the prime number theorem, I wondered whether it is ...
- 2,912
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Status of a conjecture of Hirzebruch
I was reading a paper from 1994 which claimed that the following statement was a conjecture of Hirzerbruch:
If a complex surface X is homeomorphic to either $S^2 \times S^2$ or $\mathbb{C}P^2 \# \...
- 755
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Does the sequence formed by Intersecting angle bisector in a pentagon converge?
I asked this question on MSE here.
Given a non-regular pentagon $A_1B_1C_1D_1E_1$ with no two adjacent angle having a sum of 360 degrees, from the pentagon $A_nB_nC_nD_nE_n$ construct the pentagon $...
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Conjectured primality test for specific class of $N=4kp^n+1$
Can you provide a proof or counterexample for the following claim?
Let $P_m(x)=2^{-m}\cdot((x-\sqrt{x^2-4})^m+(x+\sqrt{x^2-4})^m)$ .
Let $N= 4kp^{n}+1 $ where $k$ is a positive natural number , $...
- 2,661
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A conjecture on intersection of some intervals.
It was proved here that if $a\in \mathbb{N}_{\geq3}$ then
$$\bigcap_{i = 1}^{a} \bigcup_{j = 0}^{i-1} \left[\frac{1+aj}{i},\frac{a(j+1)-1}{i}\right] = \varnothing \tag{1}$$
It may be conjectured ...
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Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$
Let $n=am+1$ where $a $ and $m>1$ are positive integers and let $p$ be the least prime divisor of $m$. Prove that if $a<p$ and $ m \ | \ \phi(n)$ then $n$ is prime.
This question is a ...
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Strengthened version of Isoperimetric inequality with n-polygon
Let $ABCD$ be a convex quadrilateral with the lengths $a, b, c, d$ and the area $S$. The main result in our paper equivalent to:
\begin{equation} a^2+b^2+c^2+d^2 \ge 4S + \frac{\sqrt{3}-1}{\sqrt{3}}\...
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In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $
I am looking for a proof of the inequality as follows:
Conjecture: Let $A_1A_2....A_n$ be the regular polygon incribed a circle $(O)$. Let $B_1B_2....B_n$ be a polygon incribed the circle $(O)...
- 1,776
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Symmetric function transition matrix and a non-conjecture by Clifford and Stanley
Consider the transition matrix $R = \left(R_{\lambda,\mu}\right)$, defined by
$$
p_\lambda = \sum_{\mu} R_{\lambda\mu}m_\mu ,
$$
between the power-sum and the monomial basis of the ring of symmetric ...
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Why is the Simple Zeros Conjecture said to be stronger than the Riemann Hypothesis?
Let the "Simple Zeros Conjecture (SZC)" be the statement that all zeros of the Riemann zeta function are simple.
I have often heard of the statement that the SZC is stronger than the Riemann ...
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Is there any progress toward solving Gilbreath's conjecture?
Gilbreath's conjecture is a hypothesis, or a conjecture, in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the ...
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The resolution of which conjecture/problem would advance Mathematics the most? [closed]
This is an impossibly broad question, and makes the unwarranted assumption that Mathematics is a uniform field. It might make more sense to ask the same question restricted to, say, Mathematical Logic,...
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Is the Tate conjecture known for etale covers of products of curves
Let $X$ be a (smooth projective geometrically connected) surface over a finitely generated field $k$. The Tate conjecture predicts that, for $l$ a prime number invertible in $k$, the Chern class map ...
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Statement of classical Ramanujan-Petersson conjecture
I'm preparing for an expository talk on some topics in the representation theory of reductive p-adic groups, including tempered representations and Whittaker models, and as motivation I wanted to ...
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Does Vizing's conjecture hold for the infinite graphs?
In finite graph theory, there are many (in)equalities which relate the integer value of a certain graph invariant (e.g. domination or chromatic number) for the product of two finite graphs (e.g. ...
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Density of the Klarner-Rado Sequence
Consider the Klarner-Rado sequence OEIS A005658 defined by the rule: the sequence starts with 1, and if it contains $n$ it also contains $2n$, $3n+2$ and $6n+3$. According to R. Guy's popular article,...
- 17k
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A generalization of Feit–Thompson conjecture, for square-free integers
I asked the following question with my account that I have for these sites Mathematics Stack Exchange and MathOverflow. The bounty that I offered in MSE expired without answers. The post that I refer ...
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Order of magnitude of extremely abundant numbers and RH
I have always been intrigued by the fact that Riemann's hypothesis is equivalent to the assertion (you can find the scanned paper here) that the inequality $$\frac{\sigma(n)}n<e^\gamma \log\log n \...
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Is there a composite number for which this game with composite numbers never ends?
I created some "game" a couple of days ago and modified it during the last hour or so and now I want to present it to you.
Choose some natural number $>1$. If the chosen natural number is of the ...
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Percentage of Ramanujan's conjectures that were proven correct
Today I read the following brief but insightful account of Ramanujan's approach to mathematics: https://www.imsc.res.in/~rao/ramanujan/images/KSRchap3.pdf and while reading this I wondered whether we ...
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Discriminant of numerator of inverse logarithmic derivative operator iteration
Let $T:\mathbb Q(x)\to \mathbb Q(x)$ be the operator of inverse logarithmic derivative, i.e. $$Tf=\frac{f}{f'}.$$ Define $$p_n(x)=T^n\left(x-\frac{x^2}{2}\right).$$ Let $f_n(x) \in \mathbb Z[x]$ be ...
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Prime constellation conjectures
This is a simple question about terminology and provenance.
I just need to sort out the circle of conjectures that generalize and refine the twin prime conjecture.
I've encountered Polignac's ...
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Is there any relationship between Szemerédi's theorem and Sunflower conjecture?
I have observed some similar things between a reformulation of the Sunflower conjecture (see also conjecture 1.3 in Improved bounds for the sunflower lemma) and Szemerédi's theorem such that for ...
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Generalization of Legendre`s conjecture
Legendre`s conjecture states that there is always a prime between $n^2$ and $(n+1)^2$ for every natural $n$.
It is natural to create following generalization:
Is it true that for every $\...
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A conjecture generalization of Karamata inequality
Fist I observe function $f(x)=x^2$ in the figure as following
I found that when $x_1 \ge y_1$ and $x_2 \le y_2$ $\Rightarrow$ $AB \ge CD$
$\Rightarrow$ $$\frac{f(x_1)+f(x_2)}{2}-f(\frac{x_1+x_2}...
- 1,044
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Vaught conjecture for uncountable languages
Recall Vaught conjecture: the number of countable models of a first-order complete theory in a countable language is finite or $\aleph_0$ or $2^{\aleph_0}.$
Now let $\lambda$ be an uncountable ...
user39869
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About semiprimal representations of $1$
Conjecture $A_1$ : For every $m \in \mathbb N \setminus \{1\}$ there exist mutually different primes $p_{r_1},...,p_{r_m}$ and mutually different primes $b_{w_1},...,b_{w_m}$ and numbers $i_1,...,i_m \...
user153451
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What is the status of this fifty-year-old conjecture of Kostant?
On page 3.27 of his 1963 thesis on the cohomology of homogeneous spaces as approached through the Eilenberg–Moore spectral sequence, Paul Baum states the following conjecture, which he attributes to B....
- 2,995
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What will be the consequences if second Hardy-Littlewood conjecture turns out to be true?
It is generally believed that the Second Hardy-Littlewood Conjecture is false. But it has not been proved (or disproved) yet. My question is,
What would be the consequences if Second Hardy-Littlewood ...
user57432
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Graphs with graphic imbalance sequences
Let $G$ be simple undirected graph and $e=uv\in E(G)$.
The imbalance of the edge $e$ is the value $imb(e)=|d(u)-d(v)|$.
Let $M_{G}$ denotes the imbalance sequence (or more correctly, multiset of ...
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Conjectures and open problems in representation theory [closed]
Are there very famous open problems or conjectures in representation theory, or in enumerative geometry, like the volume conjecture in topology?
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Different flavours of Vassiliev Conjecture
There is something that puzzles me about "Vassiliev's Conjecture". I am sure I am missing some detail which is obvious to the community, since there are several tightly related kind of ...
- 2,152
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Zero divisors in complex group algebras of residually finite groups
Conjecture. There exists a function $f:\mathbb{N} \rightarrow \mathbb{N}$ such that if $\alpha$ and $\beta$ are non-zero elements of the complex group algebra $\mathbb{C}[G]$ of a finite group $G$ ...
- 3,738
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Lemoine-Lozada circles
I made some rookie attempt to define the 4th Lemoine circle recently. The alternative name for this circle was suggested yesterday. Further investigation revealed a family of circles associated with ...
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The 4th Lemoine circle
The first and second Lemoine circles are well-known to geometers. According to this article the third Lemoine circle has been first discovered by Jean-Pierre Ehrmann in 2002. It is worth noting that ...
- 445
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Inductively computing Mersenne primes / perfect numbers?
For two sets $A,B$ set $A+B = \{a +b | a \in A,b \in B\}$.
Let $(x_n)_{n \in \mathbb{N}}$ be independent variables. Let $\sigma(n)$ be the sum of divisors of $n$.
Set $\hat{\phi}(1) = \{x_1\}$ and ...
user6671
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Connes Embedding Conjecture and Fusion Categories
I was recently introduced to Connes' Embedding Conjecture (CEC) which states:
Every separable type $II_{1}$ factor is embeddable into $R^{\omega}$. Where $\omega$ is a generic free ultrafilter on $\...
- 547
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Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?
This question was posted in MSE in early August 2020. It did garner several upvotes, but did not receive any responses. I have therefore cross-posted it here, hoping that it gets answered.
Let $\...
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Localizing Bondy's metaconjecture on hamiltonicity
Definitions:
Let $G$ be a graph on $n$ vertices. $G$ is Hamiltonian provided $G$ has a cycle of length $n$. $G$ is pancyclic provided $G$ has a cycle of length $\ell$ for every $3 \leq \ell \leq n$.
...
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An inequality in cyclic polygon and tangential polygon
I proposed my conjecture, it is strengthened version of the Erdős–Mordell inequality as following:
Let $A_1A_2.....A_n$ be a cyclic polygon and $B_1B_2....B_n$ be the its tangential polygon. Let $P$ ...
- 1,044
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Peculiarities in low dimensions or low order or etc
I have been pondering about certain conjectures and theorems viewed as either low vs high dimensions, or smaller vs larger primes, or anything of the sort "low vs high order". Let me mention a couple ...