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The very special algebraic properties ofω give rise to an extremely rich series of results in the form of polylogarithmic ladders up to the 8th order, with a probable extension to the 9th All but three of the results forn < 5 come from Kummer's equations Atn = 5 there are seven results of which...
An upper bound is determined for the α for whichD(f)
α is a concave function off, wheref ranges over Minkowski-reduced positive definite quadratic forms inn variables with diagonal coefficients unity andD(f) denotes the determinant off In answer to a question of C E Nelson, it is shown thatD(f)...
The classical Gauss code problem asks to characterize which cyclic sequences arise as the vertex sequence of the ‘straight-ahead path of a 4-regular graph embedded in the plane This problem is generalized to certain 4 regular graphs in arbitrary surfaces
We consider a pair of MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning It is shown that a pair of MOLS withn holes of sizeh exist forh ≥ 2 if and only ifn ≥ 4 For SOLS (self-orthogonal Latin squares) with holes, we have the...
Gini, Lehmer, Beckenbach, and others studied the meanG
(a, b) = (a
s 1 +b
) We prove
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