
Recent Activity
Lindelöf hypothesis ★★
Author(s): Lindelöf


Since can be replaced by a smaller value, we can also write the conjecture as, for any positive
,
Keywords: Riemann Hypothesis; zeta
Termination of the sixth Goodstein Sequence ★
Author(s): Graham
Keywords: Goodstein Sequence
Consecutive non-orientable embedding obstructions ★★★
Author(s):

Diagonal Ramsey numbers ★★★★
Author(s): Erdos
Let denote the
diagonal Ramsey number.

Keywords: Ramsey number
The 4x5 chessboard complex is the complement of a link, which link? ★★
Author(s): David Eppstein
Keywords: knot theory, links, chessboard complex
Elementary symmetric of a sum of matrices ★★★
Author(s):
Given a Matrix , the
-th elementary symmetric function of
, namely
, is defined as the sum of all
-by-
principal minors.
Find a closed expression for the -th elementary symmetric function of a sum of N
-by-
matrices, with
by using partitions.
Keywords:
Monochromatic empty triangles ★★★
Author(s):
If is a finite set of points which is 2-colored, an empty triangle is a set
with
so that the convex hull of
is disjoint from
. We say that
is monochromatic if all points in
are the same color.




Keywords: empty triangle; general position; ramsey theory
Edge-antipodal colorings of cubes ★★
Author(s): Norine
We let denote the
-dimensional cube graph. A map
is called edge-antipodal if
whenever
are antipodal edges.



Keywords: antipodal; cube; edge-coloring
Exponential Algorithms for Knapsack ★★
Author(s): Lipton
The famous 0-1 Knapsack problem is: Given and
integers, determine whether or not there are
values
so that
The best known worst-case algorithm runs in time
times a polynomial in
. Is there an algorithm that runs in time
?
Keywords: Algorithm construction; Exponential-time algorithm; Knapsack
Unsolvability of word problem for 2-knot complements ★★★
Author(s): Gordon


Keywords: 2-knot; Computational Complexity; knot theory
Algorithm for graph homomorphisms ★★
Author(s): Fomin; Heggernes; Kratsch
Is there an algorithm that decides, for input graphs and
, whether there exists a homomorphism from
to
in time
for some constant
?
Keywords: algorithm; Exponential-time algorithm; homomorphism
Exact colorings of graphs ★★
Author(s): Erickson









Keywords: graph coloring; ramsey theory
Dividing up the unrestricted partitions ★★
Begin with the generating function for unrestricted partitions:
(1+x+x^2+...)(1+x^2+x^4+...)(1+x^3+x^6+...)...
Now change some of the plus signs to minus signs. The resulting series will have coefficients congruent, mod 2, to the coefficients of the generating series for unrestricted partitions. I conjecture that the signs may be chosen such that all the coefficients of the series are either 1, -1, or zero.
Keywords: congruence properties; partition
The stubborn list partition problem ★★
Author(s): Cameron; Eschen; Hoang; Sritharan












Keywords: list partition; polynomial algorithm
Long rainbow arithmetic progressions ★★
Author(s): Fox; Jungic; Mahdian; Nesetril; Radoicic
For let
denote the minimal number
such that there is a rainbow
in every equinumerous
-coloring of
for every


Keywords: arithmetic progression; rainbow
Reconstruction conjecture ★★★★
The deck of a graph is the multiset consisting of all unlabelled subgraphs obtained from
by deleting a vertex in all possible ways (counted according to multiplicity).

Keywords: reconstruction
Finding k-edge-outerplanar graph embeddings ★★
Author(s): Bentz



Keywords: planar graph; polynomial algorithm
Approximation ratio for k-outerplanar graphs ★★
Author(s): Bentz

Keywords: approximation algorithms; planar graph; polynomial algorithm
Approximation Ratio for Maximum Edge Disjoint Paths problem ★★
Author(s): Bentz


Keywords: approximation algorithms; Disjoint paths; planar graph; polynomial algorithm
Beneš Conjecture (graph-theoretic form) ★★★
Author(s): Beneš








Keywords: