Coverings
Coverings
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A covering is a (typically finite) set of congruence classes (r mod m) such that each integer satisfies at least one of the congruences.
Sierpiński Numbers
Sierpiński Numbers
A Sierpiński number is a positive odd integer k such that k⋅2ⁿ + 1 is composite for all positive integers n.
Newton Polygons
Newton Polygons
A polynomial with integer coefficients admits a Newton polygon that tells us a lot about its potential factorization over the integers.
The above are three research areas I am interested in that are also especially accessible as undergraduate research projects. I am also interested in the interdisciplinary overlaps between mathematics and the arts, and with music especially.
Publications
Michael Filaseta, Robert Groth, and Thomas Luckner, Generalized Sierpiński Numbers, Colloquium Mathematicum 174 (2023),191-201. (pdf)
Robert Groth, Serialism Applied to a Mathematical Curiosity: The Musical Analogue to the Smallest Known Sierpiński Number, Proceedings of Bridges 2024: Mathematics, Music, Art, Architecture, Culture, (2024), 53-60. (pdf)
Accepted
Carrie Finch-Smith, Robert Groth, and Josh Harrington, Consecutive Sierpiński Numbers, Journal of Integer Sequences (accepted)
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