On a Generalization of a Lucas' Result and an Application to the 4-Pascal's Triangle
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DOI: 10.3390/sym12020288
Abstract: The Pascal’s triangle is generalized to “the k-Pascal’s triangle” with any integer k ≥ 2 . Let p be any prime number. In this article, we prove that for any positive integers n and e,… read more here.
Keywords: triangle; lucas result; application; pascal triangle ... See more keywords
On a Surface Associated with Pascal's Triangle
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DOI: 10.3390/sym14020411
Abstract: An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients),… read more here.
Keywords: triangle; binomial coefficients; pascal triangle; associated pascal ... See more keywords