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COMBINATORICS
2007
15 years 3 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
15 years 3 months ago
2007
The distinguishing number ∆(X) of a graph X is the least positive integer n for which there exists a function f : V (X) → {0, 1, 2, · · · , n−1} such that no nonidentity ...
127
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COMBINATORICS
2007
15 years 3 months ago
2007
A k-ary necklace of order n is an equivalence class of strings of length n of symbols from {0, 1, . . . , k − 1} under cyclic rotation. In this paper we define an ordering on t...
129
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COMBINATORICS
2007
15 years 3 months ago
2007
We study the shape of the Young diagram λ associated via the Robinson– Schensted–Knuth algorithm to a random permutation in Sn such that the length of the longest decreasing ...
114
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COMBINATORICS
2007
15 years 3 months ago
2007
There are many applications of the enumeration of maps in surfaces to other areas of mathematics and the physical sciences. In particular, in quantum field theory and string theo...