COMBINATORICS
2007
13 years 4 months ago
2007
Let k3(n) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k3(7) ≥ 156 and k3(8) ≥ 402 improving on the best previou...
COMBINATORICS
2007
13 years 4 months ago
2007
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-...
COMBINATORICS
2007
13 years 4 months ago
2007
We compute the list of all minimal 2-infinite diagrams, which are cluster algebraic analogues of extended Dynkin graphs.
COMBINATORICS
2007
13 years 4 months ago
2007
COMBINATORICS
2007
13 years 4 months ago
2007
For a permutation π = π1π2 · · · πn ∈ Sn and a positive integer i ≤ n, we can view π1π2 · · · πi as an element of Si by order-preserving relabeling. The j-set of ...
COMBINATORICS
2007
13 years 4 months ago
2007
Suppose xm + axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ F∗ p. We prove that gcd(m−n, p−1) /∈ {2, 4}. In the special cas...
COMBINATORICS
2007
13 years 4 months ago
2007
A closed knight’s tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated i...
COMBINATORICS
2007
13 years 4 months ago
2007
Each m by m symmetric matrix M over 0, 1, ∗, defines a partition problem, in which an input graph G is to be partitioned into m parts with adjacencies governed by M, in the sen...
COMBINATORICS
2007
13 years 4 months ago
2007
We introduce and develop a two-parameter chromatic symmetric function for a simple graph G over the field of rational functions in q and t , Q (q, t). We derive its expansion in ...
COMBINATORICS
2007
13 years 4 months ago
2007
Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. However, if the edge-to-edge restriction is relaxed, there are othe...