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Unpacking Ross River virus trends in Queensland: Regional insights and predictive modeling. [PDF]
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Factors of Binomial Coefficients
The Mathematical Gazette, 1959If Pascal’s Triangle is written down, it will be noticed that the number of odd numbers in any row is a power of 2; moreover, if every even number is replaced by 0 and every odd number by 1, the result is an interesting pattern of triangles from which it is possible to deduce a general rule.
E. H. Lockwood, P. Gant
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A Regular Determinant of Binomial Coefficients [PDF]
Proceedings of the American Mathematical Society, 1973 Let n be a positive integer and suppose that each of {a,}' and (c,)} is an increasing sequence of nonnegative integers. Let M be the n x n matrix such that M ij=C(a,, Cj), where C(m, n) is the number of combinations of m objects taken n at a time. We give an explicit formula for the determinant of M as a sum of nonnegative quantities. Further, if ai>cj,
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2015
We now turn our attention to one of the most fundamental and useful notions in all of combinatorics, the binomial coefficient. You may recall the binomial coefficient from high-school algebra class. However, we will give several other interpretations for this concept.
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We now turn our attention to one of the most fundamental and useful notions in all of combinatorics, the binomial coefficient. You may recall the binomial coefficient from high-school algebra class. However, we will give several other interpretations for this concept.
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An Inequality on Binomial Coefficients [PDF]
, 1978 Publisher Summary The chapter discusses an inequality on binomial coefficients. The result obtained in this chapter is used to establish a result on edge-coloring of certain hypergraphs. Part of the theorem is known to Erdos, who also suggested a line of proof to establish this result for large n.
Kenneth J. Winston +2 more
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A generalization of an inequality on binomial coefficients
Rivista di Matematica per le Scienze Economiche e Sociali, 1979A generalization of an inequality on binomial coefficients solved by E. L. Johnson, D. Newman, K. Winston [1] is analyzed and at the worst the problem is reduced into the choice between two alternatives for the solutions.
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On the scarcity of powerful binomial coefficients
Mathematika, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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