Pascal’s Triangle – Knowledge and References

Pascal's Triangle

Methodological background for the mechanics of granular media

Published in I.I. Kandaurov, R.B. Zeidler, Mechanics of Granular Media and its Application in Civil Engineering, 2022

In particular, the probabilistic tower of the binomial distribution is given by the Pascal triangle. Each coefficient of the probabilistic series in this tower is equal to the sum of two overlying coefficients of the preceding series: () Cni=Cn−1i−1+Cn−1i

Combinatorics

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Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012

Walter D. Wallis

Binomial coefficients are usually presented in a triangular array, called Pascal’s Triangle (although it certainly predates Pascal; see [2] or [4], which specify earlier Chinese, Indian, and European sources). In the figure below, the entry in row n and column k is (nk).

Spectroscopy

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Published in Michael B. Smith, A Q&A Approach to Organic Chemistry, 2020

Michael B. Smith

In mathematics, Pascal’s triangle is a triangular array of the binomial coefficients. It is a triangle of numbers bordered by ones on the right and left sides. Every number inside the triangle is the sum of the two numbers directly above it: 1 + 1 = 2; 1 + 2 = 3; 1 + 3 = 4, 3 + 3 = 6, etc.

The min–max order picking problem in synchronised dynamic zone-picking systems

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Journal Information

Published in International Journal of Production Research, 2023

Serhat Saylam, Melih Çelik, Haldun Süral

The coefficients in the Binomial Expansion also correspond to the entries of Pascal’s Triangle such that the th coefficient in the Binomial expansion is equal to the entry at aisle , picker in the Pascal’s Triangle.

Pascal's Triangle

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Methodological background for the mechanics of granular media

Combinatorics

Spectroscopy

The min–max order picking problem in synchronised dynamic zone-picking systems