
Recent Activity
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











![$ X \mathrel{[ \mu]^{\ast}} Y $](/files/tex/0ef560be389646efd1fdde5ebc9afc9ac98ee64e.png)
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


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






- \item If






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







Keywords: co-completion; completion; reloid
List Total Colouring Conjecture ★★
Author(s): Borodin; Kostochka; Woodall


Keywords: list coloring; Total coloring; total graphs
Partitioning the Projective Plane ★★
Author(s): Noel
Throughout this post, by projective plane we mean the set of all lines through the origin in .









Keywords: Partitioning; projective plane