Divisibility - with visibility
type: Item
instance of: scholarly article
title: Divisibility - with visibility
zbMATH Open document ID: 0644.05002
DOI: 10.1007/BF03028359
author: Marta Sved
published in: The Mathematical Intelligencer
publication date: 1988-01-01T00:00:00Z
review text: If one reduces all the entries in the Pascal triangle of binomials modulo 2 or more generally modulo a prime number p the resulting triangle of residuals shows interesting patterns which can be visualized by the use of computer outprints. Exploiting these regularities leads to well comprehensible proofs of deeper relations for the binomials like a theorem by Lucas. This approach can then be transferred and generalized to other arrays of combinatorial numbers which obey recurrence relations of a structure similar to that for the binomials. This is demonstrated here for the Gaussian coefficients (number of subspaces in finite vector spaces) and the Stirling numbers of second kind. Aesthetically attractive computer outprints are shown further for the case of a prime power as a modulus. There are a number of open problems in these cases as there are for higher dimensional arrays (like for the multinomials).
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 4049650
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Pascal triangle
zbMATH Keywords: Gaussian coefficients
zbMATH Keywords: Stirling numbers
MaRDI profile type: Publication
cites work: Pascal (Mod p)
cites work: Binomial Coefficients Modulo a Prime
cites work: Divisibility properties of binomial coefficients
cites work: Q4740120
cites work: Q3328550
cites work: Geometry of Binomial Coefficients
description: scientific article; zbMATH DE number 4049650