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Given the importance of binomial coefficients and combinatorial sums in many areas of mathematics, it is not surprising that divisibility properties and congruences of these
Jakimczuk, A note on sums of powers which have a fixed number of prime factors,.. Jakimczuk, Desigualdades y f´ormulas asint´oticas para sumas de potencias
Since the upper bound of the area of straight-line grid drawings of planar graphs is kn 2 with k ≤ 1, it is ob- vious that the upper bound for the area of a minimum-area drawing of
He studies martingales that take self-adjoint matrix values, and he shows that the maximum eigenvalue of the martingale satisfies a tail bound similar to Freedman’s inequality..
The main objective in this section is to prove the following theorem concerning the conditional distribution of the number of edges given the colouring..
In this article we consider the sample covariance matrix formed from a sequence of indepen- dent and identically distributed random vectors from the generalized domain of attraction
Heuristically, Theorem 1 can be interpreted as saying that, for a large number of high-dimensional data vectors, as long as they have nearly the same lengths and are nearly
We prove that for symmetric Markov processes of diffusion type admitting a “carré du champ”, the Poincaré inequality is equivalent to the exponential convergence of the
