We describe the structure of the unique minimal test set T for a family of vertex cover problems. The set T corresponds to the Gröbner basis of the binomial ideal for the problem as described in [1]. While T has a surprisingly simple structure, in particular when the underlying graph is complete

Abstract. Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ np+t m) ( s) (mod p) if m, n, s, t are nonnegative integers with s, t < p. In this paper we n t aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences

this document sample than one would expect by chance. The terms are selected according to a binomial likelihood ratio test [10], comparing their occurrence in the first 20 documents to their occurrence in the rest of the collection. The selected terms are then weighted in proportion

is at least (1−ε)d/6. We also prove that for the Binomial random graph model G(n, p), for every positive ε> 0 and large enough values of K, if p> K ln n n then with high probability the local resilience of G(n, p) with respect to being Hamiltonian is at least (1 − ε)np/6. Finally, we apply similar

Abstract: The multicast operation used by MPI under Grid environment can have a substantial impact on performance of parallel applications. Since the finding of an optimal multicast operation is an NP-hard problem, a near-optimal heuristic is crucial for building an efficient MPI runtime

theory is that of the coin flip sequence. We flip a biased coin n times which is heads with probability p, and count the number of occurrences of heads, X. Clearly, X is binomially distributed with parameters n and p. While it is possible that X = n, it is elementary that this probability is vanishingly

• Combinatorics is about organization. • Many combinatorial problems involve ways to enumerate, or count, various things in an efficient manner. • The counting function C(n,k), is a powerful tool used to count subsets of a larger set, or give coefficients in binomial expansions. • Bijection

-tivariate lacunary polynomials of finite fields of large characteristic. We provide NP-hardness results to explain our inability to compute binomial factors.

in a run of RANDOMIZED-QUICKSELECT() is at most 1 n. Solution: For this problem, we will need the Chernoff bound. Theorem 1.1 Let X1, X2,..., Xn denote the indicator random variables of n Bernoulli trials, each with probability of success p. The random variable X = �n i=1 Xi is a Binomial random

after the first use of the later construction, and continuing for a total of fifteen transcripts or through the end of the corpus (whichever came first). We then used a Binomial Test to obtain the probability of sampling the observed number of tokens of the earlier construction simply by chance, before