Harry Altman

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All published works

Action	Title	Year	Authors
+ PDF Chat	Bounding finite-image strings of length $\omega^k$	2024	Harry Altman
+	Integer complexity, stability, and self-similarity.	2021	Harry Altman Juan Arias de Reyna
+	Integer complexity: Stability and self-similarity	2021	Harry Altman Juan Arias de Reyna
+	Lower sets in $\mathbb{N}^m$	2019	Harry Altman Andreas Weiermann
+ PDF Chat	Integer complexity: the integer defect	2019	Harry Altman
+	Maximum linearizations of lower sets in $\mathbb{N}^m$ with application to monomial ideals	2019	Harry Altman Andreas Weiermann
+	Integer Complexity: Algorithms and Computational Results.	2018	Harry Altman
+	Internal structure of addition chains: Well-ordering	2017	Harry Altman
+ PDF Chat	Intermediate arithmetic operations on ordinal numbers	2017	Harry Altman
+	Integer complexity: Representing numbers of bounded defect	2016	Harry Altman
+	Integer Complexity: Representing Numbers of Bounded Defect	2016	Harry Altman
+	Integer complexity: algorithms and computational results	2016	Harry Altman
+	Integer Complexity: Representing Numbers of Bounded Defect	2016	Harry Altman
+ PDF Chat	Integer complexity and well-ordering	2015	Harry Altman
+	Transfinitely iterated natural multiplication of ordinal numbers	2015	Harry Altman
+	Intermediate arithmetic operations on ordinal numbers	2015	Harry Altman
+	Intermediate arithmetic operations on ordinal numbers	2015	Harry Altman
+	Internal Structure of Addition Chains: Well-Ordering	2014	Harry Altman
+	Internal Structure of Addition Chains: Well-Ordering	2014	Harry Altman
+	Integer Complexity and Well-Ordering	2013	Harry Altman
+	Integer Complexity and Well-Ordering	2013	Harry Altman
+	Numbers with Integer Complexity Close to the Lower Bound	2012	Harry Altman Joshua Zelinsky
+ PDF Chat	Numbers with Integer Complexity Close to the Lower Bound	2012	Harry Altman Joshua Zelinsky
+	Numbers with Integer Complexity Close to the Lower Bound	2012	Harry Altman Joshua Zelinsky

Common Coauthors

Coauthor	Papers Together
Joshua Zelinsky	3
Andreas Weiermann	2
Juan Arias de Reyna	2

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Arithmetic of ordinals with applications to the theory of ordered Abelian groups	1942	Philip W. Carruth	10
+ PDF Chat	Integer complexity and well-ordering	2015	Harry Altman	6
+	Integer Complexity: Experimental and Analytical Results II	2014	Juris Čerņenoks Jānis Iraids Mārtiņš Opmanis Rihards Opmanis Kārlis Podnieks	6
+ PDF Chat	Numbers with Integer Complexity Close to the Lower Bound	2012	Harry Altman Joshua Zelinsky	5
+	Algorithms for determining integer complexity	2014	Juan Arias de Reyna J. Lune	3
+	Internal Structure of Addition Chains: Well-Ordering	2014	Harry Altman	3
+ PDF Chat	Characterizing Arithmetic Read-Once Formulae	2016	Ilya Volkovich	3
+ PDF Chat	Some transfinite natural sums	2018	Paolo Lipparini	2
+	Lower Bounds for Lucas Chains	2002	Martin Kütz	2
+	Negation can be exponentially powerful	1980	Leslie G. Valiant	2
+ PDF Chat	Unsolved Problems in Number Theory	2004	Richard K. Guy	2
+	A lower bound for the length of addition chains	1975	Arnold Schönhage	2
+ PDF Chat	The Scholz-Brauer problem on addition chains	1973	Edward G. Thurber	2
+ PDF Chat	A Lower Bound for the Scholz-Brauer Problem	1969	Kenneth B. Stolarsky	2
+	On algorithms to calculate integer complexity	2017	Katherine Cordwell Alyssa Epstein Anand Hemmady Steven J. Miller Eyvindur A. Palsson Aaditya Sharma Stefan Steinerberger Yen Nhi Truong Vu	2
+	Integer complexity: algorithms and computational results	2016	Harry Altman	2
+ PDF Chat	An infinite natural sum	2016	Paolo Lipparini	2
+	Characterizing Arithmetic Read-Once Formulae	2014	Ilya Volkovich	2
+	Internal structure of addition chains: Well-ordering	2017	Harry Altman	2
+	Integer complexity: Representing numbers of bounded defect	2016	Harry Altman	2
+ PDF Chat	Unsolved Problems in Number Theory	1994	Richard K. Guy	2
+	Integer Complexity: Algorithms and Computational Results.	2018	Harry Altman	2
+	The Extraordinary Power of Division in Straight Line Programs	2012	Peter Borwein J. L. Hobart	1
+	Exponentiation	1986	Harry Gonshor	1
+	Transfinite Zahlen	1967	Heinz Bachmann	1
+	Unsolved Problems Come of Age	1989	Richard K. Guy	1
+	Integer complexity: Stability and self-similarity	2021	Harry Altman Juan Arias de Reyna	1
+	Algorithms for determining integer complexity	2014	Juan Arias de Reyna J. Lune	1
+	On algorithms to calculate integer complexity	2017	Katherine Cordwell Alyssa Epstein Anand Hemmady Steven J. Miller Eyvindur A. Palsson Aaditya Sharma Stefan Steinerberger Yen Nhi Truong Vu	1
+	Algebraic Settings for the Problem “P ≠ NP?”	1998	Lenore Blum Felipe Cucker Michael Shub Steve Smale	1
+	Unsolved Problems in Number Theory	1981	Richard K. Guy	1
+ PDF Chat	Ordinal Types in Ramsey Theory and Well-Partial-Ordering Theory	1990	Igor Kříž Robin Thomas	1
+	On addition chains l(mn)≤l(n)−b and lower bounds for c(r)	1973	Edward G. Thurber	1
+ PDF Chat	Hausdorff ’s theorem for posets that satisfy the finite antichain property	1999	Uri Abraham Robert Bonnet	1
+	On the representation of an integer in two different bases.	1980	C.L. Stewart	1
+	Integer Complexity: Breaking the θ(n2) barrier	2008	S. Venkatesh B. R. Shankar	1
+ PDF Chat	Subtraction-Free Complexity, Cluster Transformations, and Spanning Trees	2014	Sergey Fomin Dima Grigoriev Gleb Koshevoy	1
+	On a generalization of addition chains: Addition–multiplication chains	2007	Hatem M. Bahig	1
+ PDF Chat	Orderings of monomial ideals	2004	Matthias Aschenbrenner Wai Yan Pong	1
+ PDF Chat	Zur Arithmetik der transfiniten Zahlen	1909	Ernst Jacobsthal	1
+	Counting arithmetic formulas	2015	Edinah K. Gnang Maksym Radziwiłł Carlo Sanna	1
+ PDF Chat	On the lengths of bad sequences of monomial ideals over polynomial rings	2012	Florian Pelupessy Andreas Weiermann	1
+ PDF Chat	Number theory for the ordinals with a new definition for multiplication.	1980	Harry Gonshor	1
+ PDF Chat	A Uniform Approach to Fundamental Sequences and Hierarchies	1994	Wilfried Buchholz Adam Cichon Andreas Weiermann	1
+	Integer Complexity and Well-Ordering	2013	Harry Altman	1
+	Some iterated natural sums	2015	Paolo Lipparini	1
+	Integer Complexity: Representing Numbers of Bounded Defect	2016	Harry Altman	1
+ PDF Chat	Integer complexity: the integer defect	2019	Harry Altman	1
+	Monomial Ideals and Their Decompositions	2018	W. Frank Moore Mark Rogers Sean Sather-Wagstaff	1
+	Counting arithmetic formulas	2014	Edinah K. Gnang Maksym Radziwiłł Carlo Sanna	1