Item Details

abstract

The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research.

subject

Fibonomial

Triangle

contributor

Southwick, Jeremiah T. (author)

Mason, Sarah K (committee chair)

Kirkman, Ellen (committee member)

Rouse, Jeremy A (committee member)

date

2016-05-21T08:35:53Z (accessioned)

2016-05-21T08:35:53Z (available)

2016 (issued)

degree

Mathematics (discipline)

identifier

http://hdl.handle.net/10339/59323 (uri)

language

en (iso)

publisher

Wake Forest University

title

Divisibility Conditions for Fibonomial Coefficients

type

Thesis