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Proceedings of the American Mathematical Society

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Simple proof that a $p$-adic Pascal’s triangle is $120\deg$ rotatable


Authors: Sin Hitotumatu and Daihachiro Sato
Journal: Proc. Amer. Math. Soc. 59 (1976), 406-407
MSC: Primary 10A05
DOI: https://doi.org/10.1090/S0002-9939-1976-0409325-3
MathSciNet review: 0409325
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Abstract: An array of numbers which is obtained by the replacement of binomial or multinomial coefficients by their $p$-adic valuation is not only parallel translatable but also $120^\circ$ rotatable, without changing its configuration in the Pascal’s triangle.


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Keywords: Pascal’s triangle, binomial coefficients, multinomial coefficients, <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img5.gif" ALT="$p$">-adic valuations, equal product property, equal GCD-LCM property, crystallographic groups
Article copyright: © Copyright 1976 American Mathematical Society