
Recent Activity
A funcoid related to directed topological spaces ★★
Author(s): Porton

![$ [-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\} $](/files/tex/3252019c60a83f00ff396d823dbff8040639f409.png)



![$ x\in[-\infty,+\infty] $](/files/tex/4e57a21194d8d5a659e259a111ed13a9c23b52a1.png)
If proved true, the conjecture then can be generalized to a wider class of posets.
Keywords:
Infinite distributivity of meet over join for a principal funcoid ★★
Author(s): Porton



Keywords: distributivity; principal funcoid
Weak saturation of the cube in the clique ★
Determine .
Keywords: bootstrap percolation; hypercube; Weak saturation
Convex Equipartitions with Extreme Perimeter ★★
Author(s): Nandakumar
To divide a given 2D convex region C into a specified number n of convex pieces all of equal area (perimeters could be different) such that the total perimeter of pieces is (1) maximized (2) minimized.
Remark: It appears maximizing the total perimeter is the easier problem.
Keywords: convex equipartition
Turán Problem for $10$-Cycles in the Hypercube ★★
Author(s): Erdos

Keywords: cycles; extremal combinatorics; hypercube
Extremal $4$-Neighbour Bootstrap Percolation in the Hypercube ★★

Keywords: bootstrap percolation; extremal combinatorics; hypercube; percolation
Saturation in the Hypercube ★★
Author(s): Morrison; Noel; Scott


Keywords: cycles; hypercube; minimum saturation; saturation
Cycles in Graphs of Large Chromatic Number ★★
Author(s): Brewster; McGuinness; Moore; Noel




Keywords: chromatic number; cycles
The Double Cap Conjecture ★★
Author(s): Kalai


Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere
Circular flow numbers of $r$-graphs ★★
Author(s): Steffen
A nowhere-zero -flow
on
is an orientation
of
together with a function
from the edge set of
into the real numbers such that
, for all
, and
.
A -regular graph
is a
-graph if
for every
with
odd.




Keywords: flow conjectures; nowhere-zero flows
Circular flow number of regular class 1 graphs ★★
Author(s): Steffen
A nowhere-zero -flow
on
is an orientation
of
together with a function
from the edge set of
into the real numbers such that
, for all
, and
. The circular flow number of
is inf
has a nowhere-zero
-flow
, and it is denoted by
.
A graph with maximum vertex degree is a class 1 graph if its edge chromatic number is
.





Chromatic number of associahedron ★★
Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood
Are there infinite number of Mersenne Primes? ★★★★
Author(s):
![\[ M_n = 2^p - 1 \]](/files/tex/eb18a56e5c2e8b1be6ac733d217c0c1f1a47a94e.png)
Are there infinite number of Mersenne Primes?
Keywords: Mersenne number; Mersenne prime
Are all Mersenne Numbers with prime exponent square-free? ★★★
Author(s):

Keywords: Mersenne number
What are hyperfuncoids isomorphic to? ★★
Author(s): Porton
Let be an indexed family of sets.
Products are for
.
Hyperfuncoids are filters on the lattice
of all finite unions of products.


- \item prestaroids on



If yes, is defining the inverse bijection? If not, characterize the image of the function
defined on
.
Consider also the variant of this problem with the set replaced with the set
of complements of elements of the set
.
Keywords: hyperfuncoids; multidimensional
Another conjecture about reloids and funcoids ★★
Author(s): Porton




Note: it is known that (see below mentioned online article).
Keywords:
Inequality for square summable complex series ★★
Author(s): Retkes


Keywords: Inequality
One-way functions exist ★★★★
Author(s):
Keywords: one way function
Chromatic Number of Common Graphs ★★
Author(s): Hatami; Hladký; Kráľ; Norine; Razborov
Keywords: common graph
Erdős–Straus conjecture ★★
For all , there exist positive integers
,
,
such that
.
Keywords: Egyptian fraction