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84
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COMBINATORICS
2007
15 years 19 days ago
2007
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, an...
93
Voted
COMBINATORICS
2007
15 years 19 days ago
2007
It is shown that the (diagonal) size Ramsey numbers of complete m-partite graphs Km(n) can be bounded from below by cn22(m−1)n, where c is a positive constant. Key words: Size R...
47
Voted
COMBINATORICS
2007
15 years 19 days ago
2007
In 1995, Hochberg, McDiarmid, and Saks proved that the vertex-bandwidth of the triangular grid Tn is precisely n + 1; more recently Balogh, Mubayi, and Pluh´ar posed the problem ...
63
Voted
COMBINATORICS
2007
15 years 19 days ago
2007
By combining the functional equation method with Jacobi’s triple product identity, we establish a general equation with five free parameters on the modified Jacobi theta functi...
88
Voted
COMBINATORICS
2007
15 years 19 days ago
2007
We compute the spectrum of the Schreier graph of the symmetric group Sn corresponding to the Young subgroup S2 × Sn−2 and the generating set consisting of initial reversals. In ...