View Proposal #506
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ID | 506 |
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First Name | Joshua |
Last Name | Zelinsky |
Institution | ISU |
Speaker Category | faculty |
Title of Talk | Lower and upper bounds in integer complexity. |
Abstract | Define ||n|| to be the complexity of n, the smallest number of 1's needed to write n using an arbitrary combination of addition and multiplication. John Selfridge showed that ||n|| is at least 3log3n for all n, and this lower bound is obtained exactly when n is a power of 3. Richard Guy noted the trivial upper bound of 3log_2 n for all n bigger than 1, by writing n in base 2. This talk will discuss work improving the upper bound, as well as work leading to a complete classification of numbers whose complexity is close to the lower bound. Along the way, we'll develop connections to both ordinal numbers and the p-adics. |
Subject area(s) | Number theory |
Suitable for undergraduates? | Y |
Day Preference | SaturdayStrong |
Computer Needed? | Y |
Bringing a laptop? | N |
Overhead Needed? | N |
Software requests | |
Special Needs | |
Date Submitted | 09/17/2018 |
Year | 2018 |