Pieter C. Allaart

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All published works

Action	Title	Year	Authors
+	Random subsets of Cantor sets generated by trees of coin flips	2025	Pieter C. Allaart Taylor Jones
+ PDF Chat	The $\beta$-transformation with a hole at $0$: the general case	2024	Pieter C. Allaart Derong Kong
+	On the existence of numbers with matching continued fraction and base b expansions	2023	Pieter C. Allaart Stephen Jackson Taylor Jones David L. Lambert
+	Entropy plateaus, transitivity and bifurcation sets for the $β$-transformation with a hole at $0$	2023	Pieter C. Allaart Derong Kong
+	Random subsets of Cantor sets generated by trees of coin flips	2023	Pieter C. Allaart Taylor Jones
+ PDF Chat	Box-counting dimension and differentiability of box-like statistically self-affine functions	2022	Pieter C. Allaart Taylor Jones
+ PDF Chat	Density spectrum of Cantor measure	2022	Pieter C. Allaart Derong Kong
+	Critical values for the -transformation with a hole at	2022	Pieter C. Allaart Derong Kong
+	Box-counting dimension and differentiability of box-like statistically self-affine functions	2022	Pieter C. Allaart Taylor Jones
+	Critical values for the $\beta$-transformation with a hole at $0$	2021	Pieter C. Allaart Derong Kong
+	On the existence of Trott numbers	2021	Pieter C. Allaart Stephen Jackson Taylor Jones David Lambert
+	On the existence of numbers with matching continued fraction and decimal expansions	2021	Pieter C. Allaart Stephen Jackson Taylor Jones David L. Lambert
+	Critical values for the $β$-transformation with a hole at $0$	2021	Pieter C. Allaart Derong Kong
+	On the smallest base in which a number has a unique expansion	2020	Pieter C. Allaart Derong Kong
+ PDF Chat	Relative bifurcation sets and the local dimension of univoque bases	2020	Pieter C. Allaart Derong Kong
+	The pointwise Hölder spectrum of general self-affine functions on an interval	2020	Pieter C. Allaart
+	On the smallest base in which a number has a unique expansion	2020	Pieter C. Allaart Derong Kong
+	Density spectrum of Cantor measure	2020	Pieter C. Allaart Derong Kong
+ PDF Chat	A random walk version of Robbins' problem: small horizon	2019	Pieter C. Allaart A. C. Allen
+ PDF Chat	Bifurcation sets arising from non-integer base expansions	2019	Pieter C. Allaart Simon Baker Derong Kong
+	On the continuity of the Hausdorff dimension of the univoque set	2019	Pieter C. Allaart Derong Kong
+ PDF Chat	An algebraic approach to entropy plateaus in non-integer base expansions	2019	Pieter C. Allaart
+	An algebraic approach to entropy plateaus in non-integer base expansions	2018	Pieter C. Allaart
+	A random walk version of Robbins' problem: small horizon	2018	Pieter C. Allaart A. C. Allen
+	Differentiability and Hölder spectra of a class of self-affine functions	2018	Pieter C. Allaart
+	An algebraic approach to entropy plateaus in non-integer base expansions	2018	Pieter C. Allaart
+	A random walk version of Robbins' problem: small horizon	2018	Pieter C. Allaart Andrew J. Allen
+	Differentiability and H\"older spectra of a class of self-affine functions	2017	Pieter C. Allaart
+	Differentiability of a two-parameter family of self-affine functions	2017	Pieter C. Allaart
+	On univoque and strongly univoque sets	2017	Pieter C. Allaart
+	Bifurcation sets arising from non-integer base expansions	2017	Pieter C. Allaart Simon Baker Derong Kong
+	Differentiability and Hölder spectra of a class of self-affine functions	2017	Pieter C. Allaart
+ PDF Chat	A sharp lower bound for choosing the maximum of an independent sequence	2016	Pieter C. Allaart José A. Islas
+	Differentiability of a two-parameter family of self-affine functions	2016	Pieter C. Allaart
+ PDF Chat	The infinite derivatives of Okamoto's self-affine functions: an application of $\beta$-expansions	2016	Pieter C. Allaart
+	On univoque and strongly univoque sets	2016	Pieter C. Allaart
+	On univoque and strongly univoque sets	2016	Pieter C. Allaart
+	Differentiability of a two-parameter family of self-affine functions	2016	Pieter C. Allaart
+	A sharp lower bound for choosing the maximum of an independent sequence	2015	Pieter C. Allaart José A. Islas
+	The infinite derivatives of Okamoto's self-affine functions: an application of beta-expansions	2015	Pieter C. Allaart
+	The infinite derivatives of Okamoto's self-affine functions: an application of beta-expansions	2015	Pieter C. Allaart
+	A sharp lower bound for choosing the maximum of an independent sequence	2015	Pieter C. Allaart José A. Islas
+ PDF Chat	Hausdorff dimension of level sets of generalized Takagi functions	2014	Pieter C. Allaart
+ PDF Chat	Correction and strengthening of “How large are the level sets of the Takagi function?”	2014	Pieter C. Allaart
+	On the level sets of the Takagi–van der Waerden functions	2014	Pieter C. Allaart
+ PDF Chat	Digital sum inequalities and approximate convexity of Takagi-type functions	2014	Pieter C. Allaart
+	On the level sets of the Takagi-van der Waerden functions	2013	Pieter C. Allaart
+ PDF Chat	Level sets of signed Takagi functions	2013	Pieter C. Allaart
+	Correction and strengthening of "How large are the level sets of the Takagi function?"	2013	Pieter C. Allaart
+	Correction and strengthening of "How large are the level sets of the Takagi function?"	2013	Pieter C. Allaart
+	On the level sets of the Takagi-van der Waerden functions	2013	Pieter C. Allaart
+	Level sets of signed Takagi functions	2012	Pieter C. Allaart
+ PDF Chat	Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’	2012	Pieter C. Allaart
+ PDF Chat	Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’	2012	Pieter C. Allaart
+	Digital sum inequalities and approximate convexity of Takagi-type functions	2012	Pieter C. Allaart
+ PDF Chat	How large are the level sets of the Takagi function?	2012	Pieter C. Allaart
+	The Takagi Function: a Survey	2012	Pieter C. Allaart Kiko Kawamura
+	Level sets of signed Takagi functions	2012	Pieter C. Allaart
+	Digital sum inequalities and approximate convexity of Takagi-type functions	2012	Pieter C. Allaart
+	The finite cardinalities of level sets of the Takagi function	2011	Pieter C. Allaart
+	The Takagi function: a survey	2011	Pieter C. Allaart Kiko Kawamura
+	The finite cardinalities of level sets of the Takagi function	2011	Pieter C. Allaart
+ PDF Chat	An inequality for sums of binary digits, with application to Takagi functions	2011	Pieter C. Allaart
+	On the distribution of the cardinalities of level sets of the Takagi function	2011	Pieter C. Allaart
+	The Takagi function: a survey	2011	Pieter C. Allaart Kiko Kawamura
+ PDF Chat	A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk	2010	Pieter C. Allaart
+ PDF Chat	A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk	2010	Pieter C. Allaart
+	An inequality for sums of binary digits, with application to Takagi functions	2010	Pieter C. Allaart
+ PDF Chat	The improper infinite derivatives of Takagi's nowhere-differentiable function	2010	Pieter C. Allaart Kiko Kawamura
+	The improper infinite derivatives of Takagi's nowhere-differentiable function	2010	Pieter C. Allaart Kiko Kawamura
+	An inequality for sums of binary digits, with application to Takagi functions	2010	Pieter C. Allaart
+	A "bang-bang" principle for predicting the supremum of a random walk or Le'vy process	2009	Pieter C. Allaart
+	A general "bang-bang" principle for predicting the maximum of a random walk	2009	Pieter C. Allaart
+ PDF Chat	On a flexible class of continuous functions with uniform local structure	2009	Pieter C. Allaart
+ PDF Chat	Injectivity of the Dubins-Freedman construction of random distributions	2009	Pieter C. Allaart R. Daniel Mauldin
+	A general "bang-bang" principle for predicting the maximum of a random walk	2009	Pieter C. Allaart
+	Predicting the supremum: optimality of "stop at once or not at all"	2009	Pieter C. Allaart
+	Distribution of the maxima of random Takagi functions	2008	Pieter C. Allaart
+	A Polynomial Fixed-Point Problem	2008	Pieter C. Allaart R. Daniel Mauldin
+ PDF Chat	Prophet Inequalities for I.I.D. Random Variables with Random Arrival Times	2007	Pieter C. Allaart
+	Dimensions of the coordinate functions of space-filling curves	2007	Pieter C. Allaart Kiko Kawamura
+	Prophet inequalities for i.i.d. random variables with random arrival times	2006	Pieter C. Allaart
+	Prophet Regions for Discounted, Uniformly Bounded Random Variables	2006	Pieter C. Allaart
+	Extreme values of some continuous nowhere differentiable functions	2006	Pieter C. Allaart Kiko Kawamura
+ PDF Chat	On the Coordinate Functions of Lévy's Dragon Curve	2006	Pieter C. Allaart Kiko Kawamura
+	Prophet inequalities for i.i.d. random variables with random arrival times	2006	Pieter C. Allaart
+	Stopping the maximum of a correlated random walk, with cost for observation	2004	Pieter C. Allaart
+	Stopping the maximum of a correlated random walk, with cost for observation	2004	Pieter C. Allaart
+	None	2003	Pieter C. Allaart
+	Optimal stopping rules for directionally reinforced processes	2001	Pieter C. Allaart Michael Monticino
+	Inequalities relating maximal moments to other measures of dispersion	2000	Pieter C. Allaart
+	A Sharp Nonconvexity Bound for Partition Ranges of Vector Measures with Atoms	1999	Pieter C. Allaart
+	Bounds on the non-convexity of ranges of vector measures with atoms	1999	Pieter C. Allaart
+	Minimax Risk Inequalities for the Location–Parameter Classification Problem	1998	Pieter C. Allaart
+	An invariant-sum characterization of Benford's law	1997	Pieter C. Allaart
+ PDF Chat	An invariant-sum characterization of Benford's law	1997	Pieter C. Allaart

Common Coauthors

Coauthor	Papers Together
Derong Kong	13
Kiko Kawamura	8
Taylor Jones	7
José A. Islas	3
Simon Baker	2
Stephen Jackson	2
A. C. Allen	2
R. Daniel Mauldin	2
David L. Lambert	2
Stephen Jackson	1
David Lambert	1
Andrew J. Allen	1
Michael Monticino	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	A simple example of the continuous function without derivative	1990	Teiji Takagi	21
+ PDF Chat	Fractal Geometry: Mathematical Foundations and Applications.	1990	K. J. Falconer	14
+ PDF Chat	Unique Representations of Real Numbers in Non-Integer Bases	2001	Paul Glendinning Nikita Sidorov	14
+	On theβ-expansions of real numbers	1960	William Parry	13
+	Unique expansions of real numbers	2009	Martijn de Vries Vilmos Komornik	10
+	On the topological structure of univoque sets	2006	Vilmos Komornik Paola Loreti	10
+	Hausdorff dimension of univoque sets and Devil's staircase	2016	Vilmos Komornik Derong Kong Wenxia Li	10
+ PDF Chat	Multifractal structure of Bernoulli convolutions	2011	Thomas Jordan Pablo Shmerkin Boris Solomyak	10
+ PDF Chat	Hausdorff dimension of unique beta expansions	2014	Derong Kong Wenxia Li	9
+ PDF Chat	How large are the level sets of the Takagi function?	2012	Pieter C. Allaart	9
+	Irregular 1-sets on the graphs of continuous functions	2008	Zoltán Buczolich	9
+	Level sets of the Takagi function: Hausdorff dimension	2009	Zachary Maddock	9
+ PDF Chat	Level sets of the Takagi function: local level sets	2012	Jeffrey C. Lagarias Zachary Maddock	9
+	None	2002	Vilmos Komornik Paola Loreti	8
+ PDF Chat	The infinite derivatives of Okamoto's self-affine functions: an application of $\beta$-expansions	2016	Pieter C. Allaart	7
+	Almost Every Number Has a Continuum of b-Expansions	2003	Nikita Sidorov	7
+	Generalised golden ratios over integer alphabets	2014	Simon Baker	7
+	On univoque and strongly univoque sets	2017	Pieter C. Allaart	7
+	A Simple Continuous Function with a Finite Derivative at No Point	1933	Toni Hildebrandt	7
+ PDF Chat	Intersections of homogeneous Cantor sets and beta-expansions	2010	Derong Kong Wenxia Li F. M. Dekking	7
+	An Introduction to Symbolic Dynamics and Coding	2010	Douglas Lind Brian Marcus	7
+ PDF Chat	Level sets of the Takagi function: generic level sets	2011	Zachary Maddock Jeffrey C. Lagarias	7
+	On the improper derivatives of Tagaki's continuous nowhere dierentiable function	2010	Manfred Krüppel	7
+ PDF Chat	On the bifurcation set of unique expansions	2019	Charlene Kalle Derong Kong Wenxia Li Fan Lü	6
+ PDF Chat	A remark on continuous, nowhere differentiable functions	2005	Hisashi Okamoto	6
+	Entropy, topological transitivity, and dimensional properties of unique 𝑞-expansions	2017	Rafael Alcaraz Barrera Simon Baker Derong Kong	6
+ PDF Chat	On the critical case of Okamoto’s continuous non-differentiable functions	2009	Kenta Kobayashi	6
+ PDF Chat	Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems	1990	Pál Erdös Istvá n Joó Vilmos Komornik	6
+ PDF Chat	Relative bifurcation sets and the local dimension of univoque bases	2020	Pieter C. Allaart Derong Kong	6
+	The Hausdorff dimension of the level sets of Takagi’s function	2011	Enrique de Amo Imen Bhouri Manuel Díaz Carrillo Juan Fernández Sánchez	6
+	Van der Waerden's Continuous Nowhere Differentiable Function	1982	Patrick Billingsley	6
+ PDF Chat	Dynamics of continued fractions and kneading sequences of unimodal maps	2012	Claudio Bonanno Carlo Carminati Stefano Isola Giulio Tiozzo	6
+	The Takagi function and its properties	2012	C. Lagarias	6
+ PDF Chat	On the classification of self-similar sets determined by two contractions on the plane	2002	Kiko Kawamura	5
+	An Elementary Example of a Continuous Non-Differentiable Function	1927	Fred W. Perkins	5
+ PDF Chat	An inequality for the Takagi function	2008	Zoltán Boros	5
+ PDF Chat	On maxima of Takagi-van der Waerden functions	1984	Yoshikazu Baba	5
+	Topology of the set of univoque bases	2016	Martijn de Vries Vilmos Komornik Paola Loreti	5
+	The Komornik-Loreti Constant is Transcendental	2000	Jean‐Paul Allouche Michel Cosnard	5
+ PDF Chat	On level sets of a continuous nowhere monotone function	1963	K. M. Garg	5
+	Continuous Nowhere-Differentiable Functions--an Application of Contraction Mappings	1991	Hidefumi Katsuura	5
+	Takagi functions and approximate midconvexity	2009	Jacek Tabor Józef Tabor	5
+	Optimal prediction of the ultimate maximum of Brownian motion	2003	Jesper Lund Pedersen	5
+	On the uniqueness of the expansions 333-01333-01333-01	1991	P. Erdős Miklós Horváth I. Joó	4
+ PDF Chat	On multifractality and time subordination for continuous functions	2008	Stéphane Seuret	4
+	The Takagi Function: a Survey	2012	Pieter C. Allaart Kiko Kawamura	4
+ PDF Chat	Bifurcation sets arising from non-integer base expansions	2019	Pieter C. Allaart Simon Baker Derong Kong	4
+	Greedy and quasi-greedy expansions in non-integer bases	2007	Claudio Baiocchi Vilmos Komornik	4
+ PDF Chat	On Hausdorff dimension of invariant sets for expanding maps of a circle	1986	Mariusz Urbański	4
+	On Hildebrandt's Example of a Function Without a Finite Derivative	1936	E. G. Begle W. L. Ayres	4