Results 1 
4 of
4
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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
Introduction Counting Triangulations of a Convex Polygon
"... problem of counting the number of triangulations of a convex polygon. Euler, one of the most ..."
Abstract
 Add to MetaCart
problem of counting the number of triangulations of a convex polygon. Euler, one of the most
Gabriel Lam'e's Counting of Triangulations
"... studied earlier by the prolific Leonhard Euler (17071783), can be stated as follows. Given a convex nsided polygon, divide it into triangles by drawing nonintersecting diagonals connecting some of the vertices of the polygon. Euler calculated the number, Pn, of distinct triangulations of a convex ..."
Abstract
 Add to MetaCart
studied earlier by the prolific Leonhard Euler (17071783), can be stated as follows. Given a convex nsided polygon, divide it into triangles by drawing nonintersecting diagonals connecting some of the vertices of the polygon. Euler calculated the number, Pn, of distinct triangulations of a convex ngon for the first few values of n, and conjectured a formula for Pn based on an empirical study of the ratios Pn+1/Pn [1, p. 339 350] [2]. Lam'e was one of the first to provide the details for a combinatorial proof of Euler's conjectured result for Pn+1/Pn, a proof which the reader will study in its original (translated) version in this project.
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 ..."
Abstract
 Add to MetaCart
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