Harry J. Altman

activity

20122026

most citedInteger complexity: The integer defect

3 citations · 7 across the 5 of their papers we have counts for

collaborators

Showing math.NTShow all

7 papers · 1 filter

math.NT2021

Integer complexity: Stability and self-similarity

Harry Altman, Juan Arias de Reyna

Define $∣∣ n ∣∣$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. The set $D$ of…

math.NT2018★ 3 cited

Integer complexity: The integer defect

Harry Altman

Define $∥ n ∥$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed tha…

math.NT2016★ 3 cited

Integer complexity: algorithms and computational results

Harry Altman

Define $∥ n ∥$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. Define $n$ to be stable i…

math.NT2016

Integer Complexity: Representing Numbers of Bounded Defect

Harry Altman

Define $∥ n ∥$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed tha…

math.NT2014

Internal Structure of Addition Chains: Well-Ordering

Harry Altman

An addition chain for $n$ is defined to be a sequence $(a_{0}, a_{1}, \dots, a_{r})$ such that $a_{0} = 1$ , $a_{r} = n$ , and, for any $1 \leq k \leq r$ , there exist $0 \leq i, j < k$ such that $a_k = a_i…

math.NT2013

Integer Complexity and Well-Ordering

Harry Altman

Define $∥ n ∥$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed tha…

math.NT2012

Numbers with Integer Complexity Close to the Lower Bound

Harry Altman, Joshua Zelinsky

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 $…