COMBINATORICS
2007
13 years 11 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 11 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 11 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 11 months ago
2007
COMBINATORICS
2007
13 years 11 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 11 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 11 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 11 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 11 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 11 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...