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Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
MULTIVARIATE FUSSCATALAN NUMBERS J.C. AVAL
, 711
"... Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan trian ..."
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Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan triangle”, a lowertriangular twodimensional array. It is surprising that the extension of this construction to 3 dimensions generates integers B3(n, k, l) that give a 2parameter distribution of C3(n) = 1
Introduction Counting Triangulations of a Convex Polygon
"... problem of counting the number of triangulations of a convex polygon. Euler, one of the most ..."
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problem of counting the number of triangulations of a convex polygon. Euler, one of the most