Recent Activity
The 3n+1 conjecture ★★★
Author(s): Collatz
Keywords: integer sequence
List Hadwiger Conjecture ★★
Author(s): Kawarabayashi; Mohar
Keywords: Hadwiger conjecture; list colouring; minors
Lucas Numbers Modulo m ★★
Author(s):
Keywords: Lucas numbers
Divisibility of central binomial coefficients ★★
Author(s): Graham
Keywords:
¿Are critical k-forests tight? ★★
Author(s): Strausz
Let be a -uniform hypergraph. If is a critical -forest, then it is a -tree.
Keywords: heterochromatic number
Saturated $k$-Sperner Systems of Minimum Size ★★
Author(s): Morrison; Noel; Scott
Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system
List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★
Author(s): Allagan
Keywords: complete bipartite graph; complete multipartite graph; list coloring
Generalised Empty Hexagon Conjecture ★★
Author(s): Wood
Keywords: empty hexagon
General position subsets ★★
Author(s): Gowers
Forcing a 2-regular minor ★★
Keywords: minors
Fractional Hadwiger ★★
Author(s): Harvey; Reed; Seymour; Wood
(a)
(b)
(c) .
Keywords: fractional coloring, minors
Generalized path-connectedness in proximity spaces ★★
Author(s): Porton
Let be a proximity.
A set is connected regarding iff .
- \item is connected regarding . \item For every there exists a totally ordered set such that , , and for every partion of into two sets , such that , we have .
Keywords: connected; connectedness; proximity space
Direct proof of a theorem about compact funcoids ★★
Author(s): Porton
The main purpose here is to find a direct proof of this conjecture. It seems that this conjecture can be derived from the well known theorem about existence of exactly one uniformity on a compact set. But that would be what I call an indirect proof, we need a direct proof instead.
The direct proof may be constructed by correcting all errors an omissions in this draft article.
Direct proof could be better because with it we would get a little more general statement like this:
- \item ; \item .
Then .
Keywords: compact space; compact topology; funcoid; reloid; uniform space; uniformity
Dirac's Conjecture ★★
Author(s): Dirac
Keywords: point set
Roller Coaster permutations ★★★
Let denote the set of all permutations of . Let and denote respectively the number of increasing and the number of decreasing sequences of contiguous numbers in . Let denote the set of subsequences of with length at least three. Let denote .
A permutation is called a Roller Coaster permutation if . Let be the set of all Roller Coaster permutations in .
- \item If , then . \item If , then with .
- \item If , then is odd for . \item If , then for all .
Keywords:
Graphs of exact colorings ★★
Author(s):
Conjecture For , let be the statement that given any exact -coloring of the edges of a complete countably infinite graph (that is, a coloring with colors all of which must be used at least once), there exists an exactly -colored countably infinite complete subgraph. Then is true if and only if , , or .
Keywords:
Imbalance conjecture ★★
Author(s): Kozerenko
Keywords: edge imbalance; graphic sequences
Every metamonovalued reloid is monovalued ★★
Author(s): Porton
Keywords:
Every metamonovalued funcoid is monovalued ★★
Author(s): Porton
The reverse is almost trivial: Every monovalued funcoid is metamonovalued.
Keywords: monovalued
Decomposition of completions of reloids ★★
Author(s): Porton
- \item if is a co-complete reloid; \item if is a complete reloid; \item ; \item ; \item .
Keywords: co-completion; completion; reloid