Recent Activity
A funcoid related to directed topological spaces ★★
Author(s): Porton
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):
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 ; \item staroids on ; \item completary staroids 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