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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
All HMC Faculty Publications and Research
We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.
Enhancement On Counting Invariant On Symmetric Virtual Biracks, Melinda Ho
Enhancement On Counting Invariant On Symmetric Virtual Biracks, Melinda Ho
Scripps Senior Theses
This thesis introduces a new enhancement for virtual birack counting invariants. We first introduce knots and other general types of knots (oriented knots, framed knots, racks, and biracks). Then we’ll discuss the methods, knot invariants, mathematicians use to identify whether two knots are different. Next we’ll look at knots with virtual crossings and knots with a good involution. Finally, we introduce a new symmetric enhancement for virtual birack counting invariants and provide an example.