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101
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COMBINATORICS
2007
15 years 3 months 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...
112
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COMBINATORICS
2007
15 years 3 months 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...
COMBINATORICS
2007
15 years 3 months 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 ...
COMBINATORICS
2007
15 years 3 months 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...
104
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COMBINATORICS
2007
15 years 3 months 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 ...