Steven Senger

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All published works

Action	Title	Year	Authors
+ PDF Chat	Pinned Dot Product Set Estimates	2024	Peter Bright Caleb Marshall Steven Senger
+ PDF Chat	Bounds on distinct and repeated dot product trees	2024	Aaron Autry Slade Gunter Christopher Housholder Steven Senger
+ PDF Chat	More on the number of distinct values of a class of functions	2024	Robert W. S. Coulter Steven Senger
+ PDF Chat	Packing sets in Euclidean space by affine transformations	2024	Alex Iosevich Pertti Mattila Eyvindur A. Palsson Minh-Quy Pham Thang Pham Steven Senger Chun‐Yen Shen
+ PDF Chat	On the solvability of systems of equations revisited	2024	Thang Pham Steven Senger Nguyen Trung-Tuan Nguyen Duc-Thang Lê Anh Vinh
+	Geometric structures in pseudo-random graphs	2024	Thang Pham Steven Senger Michael Tait Vu Thi Huong Thu
+	Improved incidence bounds over arbitrary finite fields via the VC-dimension theory	2024	Alex Iosevich Thang Pham Steven Senger Michael Tait
+	Distribution of pinned distance trees in the plane <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math>	2023	Thang Pham Steven Senger The Dung Tran
+ PDF Chat	Convexity, superquadratic growth, and dot products	2023	Brandon Hanson Oliver Roche‐Newton Steven Senger
+	An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory	2023	Alex Iosevich Thang V. Pham Steven Senger Michael Tait
+	VC-dimension and pseudo-random graphs	2023	Thang V. Pham Steven Senger Michael Tait Nguyen Thu-Huyen
+	Multi-parameter Szemerédi-Trotter-type theorems and applications in finite fields	2023	Hung Le Steven Senger Minh-Quan Vo
+ PDF Chat	On the Number of Dot Product Chains in Finite Fields and Rings	2022	Vincent Blevins David L. Crosby Ethan Lynch Steven Senger
+	The Erdos-Falconer distance problem in the tree setting	2022	Thang V. Pham Steven Senger Dung The Tran
+	Geometric structures in pseudo-random graphs	2022	Thang V. Pham Steven Senger Michael Tait Vu Thi Huong Thu
+	Angle chains and pinned variants	2021	Eyvindur A. Palsson Steven Senger Charles Wolf
+ PDF Chat	Bounds on Point Configurations Determined by Distances and Dot Products	2021	Slade Gunter Eyvindur A. Palsson Ben Rhodes Steven Senger
+	Angle chains and pinned variants	2021	Eyvindur A. Palsson Steven Senger Charles Wolf
+	On the number of dot product chains in finite fields and rings	2021	Vincent Blevins David L. Crosby Ethan Lynch Steven Senger
+	Convexity, Superquadratic Growth, and Dot Products	2021	Brandon Hanson Oliver Roche‐Newton Steven Senger
+	Bounds on point configurations determined by distances and dot products	2020	Slade Gunter Eyvindur A. Palsson Ben Rhodes Steven Senger
+	Dot product chains	2020	Shelby Kilmer Caleb Marshall Steven Senger
+	Falconer-type estimates for dot products	2020	Alex Iosevich Steven Senger
+	Bounds on point configurations determined by distances and dot products	2020	Slade Gunter Eyvindur A. Palsson Ben Rhodes Steven Senger
+	Dot product chains	2020	Shelby Kilmer Caleb Marshall Steven Senger
+	A General Framework for Studying Finite Rainbow Configurations	2019	Mike Desgrottes Steven Senger David Soukup Zhu Ren-jun
+ PDF Chat	Dimensional lower bounds for Falconer type incidence theorems	2019	Jonathan DeWitt Kevin Ford Eli Goldstein Steven J. Miller Gwyneth Moreland Eyvindur A. Palsson Steven Senger
+	Uniqueness of Optimal Point Sets Determining Two Distinct Triangles	2019	Hazel N. Brenner James S. Depret-Guillaume Eyvindur A. Palsson Steven Senger
+	On the Number of Discrete Chains	2019	Eyvindur A. Palsson Steven Senger Adam Sheffer
+	Uniqueness of Optimal Point Sets Determining Two Distinct Triangles	2019	Hazel N. Brenner James S. Depret-Guillaume Eyvindur A. Palsson Steven Senger
+	On the Number of Discrete Chains	2019	Eyvindur A. Palsson Steven Senger Adam Sheffer
+ PDF Chat	Optimal order Jackson type inequality for scaled Shepard approximation	2017	Steven Senger Xingping Sun Zongmin Wu
+	Optimal order Jackson type inequality for scaled Shepard approximation	2017	Steven Senger Xingping Sun Zongmin Wun
+	Rainbow triangles	2017	Steven Senger
+ PDF Chat	Pairs of Dot Products in Finite Fields and Rings	2017	David Covert Steven Senger
+	Optimal order Jackson type inequality for scaled Shepard approximation	2017	Steven Senger Xingping Sun Zongmin Wun
+	Rainbow triangles	2017	Steven Senger
+	Sharpness of Falconer's (d+1)/2 estimate	2016	Alex Iosevich Steven Senger
+	Upper bounds on pairs of dot products	2015	Daniel W. Barker Steven Senger
+	Upper bounds on pairs of dot products	2015	Daniel W. Barker Steven Senger
+	Pairs of dot products in finite fields and rings	2015	David S. Covert Steven Senger
+	A NOTE ON THE MULTIPLICATIVE STRUCTURE OF AN ADDITIVELY SHIFTED PRODUCT SET AA + 1	2014	Steven Senger
+ PDF Chat	On the Number of Distinct Values of a Class of Functions with Finite Domain	2014	Robert S. Coulter Steven Senger
+	Sharpness of Falconer’s Estimate and the Single Distance Problem in $$\mathbb{Z}_{q}^{d}$$	2014	Alex Iosevich Steven Senger
+	Two Combinatorial Geometric Problems Involving Modular Hyperbolas	2013	Mizan R. Khan Richard Magner Steven Senger Arne Winterhof
+	Two Combinatorial Geometric Problems Involving Modular Hyperbolas	2013	Mizan R. Khan Richard Magner Steven Senger Arne Winterhof
+	On the number of distinct values of a class of functions with finite domain	2012	Robert S. Coulter Steven Senger
+	A note on the multiplicative structure of an additively shifted product set, AA+1	2012	Steven Senger
+	On sets of directions determined by subsets of ℝ d	2012	Alex Iosevich Mihalis Mourgoglou Steven Senger
+	Distance Graphs in Vector Spaces Over Finite Fields	2012	Derrick Hart Alex Iosevich Doowon Koh Steven Senger Ignacio Uriarte-Tuero
+	On the number of distinct values of a class of functions with finite domain	2012	Robert W. S. Coulter Steven Senger
+	A note on the multiplicative structure of an additively shifted product set, AA+1	2012	Steven Senger
+	Reliability of swarming algorithms for mobile sensor network applications	2012	Steven Senger
+	EXPLORATIONS OF THE ERD } OS-FALCONER DISTANCE PROBLEM AND RELATED APPLICATIONS	2011	Steven Senger Alex Iosevich
+ PDF Chat	A Furstenberg–Katznelson–Weiss type theorem on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-point configurations in sets of positive density in finite field geometries	2010	David Covert Derrick Hart Alex Iosevich Steven Senger Ignacio Uriarte-Tuero
+ PDF Chat	Jensen’s inequality	2010	Julia Garibaldi Alex Iosevich Steven Senger
+	Hyperbolas in the plane	2010	Julia Garibaldi Alex Iosevich Steven Senger
+ PDF Chat	Applications of the Erdős distance problem	2010	Julia Garibaldi Alex Iosevich Steven Senger
+	The Cauchy-Schwarz inequality	2010	Julia Garibaldi Alex Iosevich Steven Senger
+	On sets of directions and angles determined by subsets of ${\Bbb R}^d$	2010	Alex Iosevich Steven Senger Mihalis Mourgoglou
+	A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries	2010	David Covert Derrick Hart Alex Iosevich Steven Senger Ignacio Uriarte-Tuero
+	On sets of directions determined by subsets of ${\Bbb R}^d$	2010	Alex Iosevich Mihalis Mourgoglou Steven Senger
+	Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains	2010	Alex Iosevich Steven Senger
+	A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries	2010	David S. Covert Derrick Hart Alex Iosevich Steven Senger Ignacio Uriarte-Tuero
+	On sets of directions determined by subsets of ${\Bbb R}^d$	2010	Alex Iosevich Mihalis Mourgoglou Steven Senger
+	Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains	2010	Alex Iosevich Steven Senger
+ PDF Chat	ErdoÌ‹s distance problem in the hyperbolic half-plane	2009	Steven Senger
+	A low complexity replacement scheme for erased frame coefficients	2009	Bernhard G. Bodmann Peter G. Casazza Gitta Kutyniok Steven Senger
+	Erdohs distance problem in the hyperbolic half-plane	2009	Steven Senger
+ PDF Chat	Orthogonal Systems in Vector Spaces over Finite Fields	2008	Alex Iosevich Steven Senger
+	Definability in the Existential Theory of Concatenation and Undecidable Extensions of this Theory	1988	J Büchi Steven Senger

Common Coauthors

Coauthor	Papers Together
Alex Iosevich	22
Eyvindur A. Palsson	11
Derrick Hart	4
Thang V. Pham	4
Ignacio Uriarte-Tuero	4
Michael Tait	4
Slade Gunter	4
Mihalis Mourgoglou	4
David Covert	3
Xingping Sun	3
Thang Pham	3
Caleb Marshall	3
Julia Garibaldi	3
Charles Wolf	2
Brandon Hanson	2
Ethan Lynch	2
Zongmin Wun	2
Adam Sheffer	2
Ben Rhodes	2
Arne Winterhof	2
Daniel W. Barker	2
Vincent Blevins	2
Mizan R. Khan	2
Richard Magner	2
Robert W. S. Coulter	2
James S. Depret-Guillaume	2
David S. Covert	2
Hazel N. Brenner	2
Robert S. Coulter	2
Shelby Kilmer	2
Vu Thi Huong Thu	2
David L. Crosby	2
Oliver Roche‐Newton	2
Nguyen Duc-Thang	1
Thang Pham	1
Ben Rhodes	1
Zongmin Wu	1
Julia Garibaldi	1
Doowon Koh	1
Minh-Quan Vo	1
Bernhard G. Bodmann	1
Kevin Ford	1
Thang Pham	1
J Büchi	1
Zhu Ren-jun	1
Lê Anh Vinh	1
Pertti Mattila	1
Mike Desgrottes	1
Chun‐Yen Shen	1
David Soukup	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Research Problems in Discrete Geometry	2005	János Pach Peter Braß W. O. J. Moser	12
+	On Sets of Distances of <i>n</i> Points	1970	P. Erdős	10
+	Extremal problems in discrete geometry	1983	Endre Szemerédi W. T. Trotter	8
+	Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets	1987	Pertti Mattila	8
+	Unit distances in the Euclidean plane	1984	Joel Spencer Endre Szemerédi WT Trotter	8
+	Erdös distance problem in vector spaces over finite fields	2007	Alex Iosevich M. Rudnev	8
+	None	1999	Thomas Wolff	8
+	Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics	2004	Steve Hofmann Alex Iosevich	7
+	Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdős-Falconer distance conjecture	2010	Derrick Hart Alex Iosevich Doowon Koh Misha Rudnev	7
+ PDF Chat	Finite chains inside thin subsets of ℝd	2016	Michael A. Bennett Alex Iosevich Krystal Taylor	7
+	None	2005	M. Burak Erdoğan	6
+ PDF Chat	Theory of Dimension for Large Discrete Sets and Applications	2014	Alex Iosevich M. Rudnev Ignacio Uriarte-Tuero	5
+	Channel assignment on Cayley graphs	2010	Patrick Bahls	5
+ PDF Chat	Orthogonal Systems in Vector Spaces over Finite Fields	2008	Alex Iosevich Steven Senger	5
+	On Some Exponential Sums	1948	André Weil	5
+	Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains	2010	Alex Iosevich Steven Senger	4
+ PDF Chat	On the Erdős distinct distances problem in the plane	2014	Larry Guth Nets Hawk Katz	4
+ PDF Chat	K-distance Sets, Falconer Conjecture, and Discrete Analogs	2005	Alex Iosevich Izabella Łaba	4
+ PDF Chat	On the Hausdorff dimensions of distance sets	1985	K. J. Falconer	4
+ PDF Chat	A semi-algebraic version of Zarankiewicz's problem	2017	Jacob Fox János Pach Adam Sheffer Andrew Suk Joshua Zahl	4
+	Ergodic Theory and Configurations in Sets of Positive Density	1990	Hillel Fürstenberg Yitzchak Katznelson Benjamin Weiss	4
+ PDF Chat	Breaking the 3/2 Barrier for Unit Distances in Three Dimensions	2018	Joshua Zahl	4
+ PDF Chat	A sum-product estimate in finite fields, and applications	2004	Jean Bourgain Nets Hawk Katz Terence Tao	4
+	Geometry of Sets and Measures in Euclidean Spaces	1995	Pertti Mattila	4
+	On the Hausdorff dimension and capacities of intersections	1985	Pertti Mattila	4
+ PDF Chat	Geometric incidence theorems via Fourier analysis	2009	Alex Iosevich Hadi Jorati Izabella Łaba	4
+	Pseudo-random Graphs	2006	Michael Krivelevich Benny Sudakov	4
+	A szemerédi type theorem for sets of positive density inR k	1986	Jean Bourgain	4
+	None	2003	John J. Benedetto Matthew Fickus	4
+	Integral points on strictly convex closed curves	1977	Sergeĭ Konyagin	4
+	Upper bounds on pairs of dot products	2015	Daniel W. Barker Steven Senger	4
+ PDF Chat	Ubiquity of simplices in subsets of vector spaces over finite fields	2008	Derrick Hart Alex Iosevich	3
+ PDF Chat	Pinned distance sets, k-simplices, Wolff’s exponent in finite fields and sum-product estimates	2011	Jeremy Chapman M. Burak Erdoğan Derrick Hart Alex Iosevich Doowon Koh	3
+	Directions in combinatorial geometry	2005	János Pach	3
+	Recurrence in Ergodic Theory and Combinatorial Number Theory	1981	Harry Furstenberg	3
+	An application of ergodic theory to a problem in geometric ramsey theory	1999	Tamar Ziegler	3
+	Regularity of Distance Measures and Sets	1999	Pertti Mattila Per Sjölin	3
+ PDF Chat	Distance Measures for Well-Distributed Sets	2007	Alex Iosevich M. Rudnev	3
+	On the Number of Discrete Chains	2019	Eyvindur A. Palsson Steven Senger Adam Sheffer	3
+ PDF Chat	LONG PATHS IN THE DISTANCE GRAPH OVER LARGE SUBSETS OF VECTOR SPACES OVER FINITE FIELDS	2016	Michael A. Bennett Jeremy Chapman David Covert Derrick Hart Alex Iosevich Jonathan Pakianathan	3
+ PDF Chat	Recent work connected with the Kakeya problem	2003	Thomas Wolff	3
+	On distance sets of large sets of integer points	2008	Ákos Magyar	3
+	Hausdorff dimension and distance sets	1994	Jean Bourgain	3
+	The geometry of fractal sets	1985	K. J. Falconer	3
+ PDF Chat	FREIMAN THEOREM, FOURIER TRANSFORM AND ADDITIVE STRUCTURE OF MEASURES	2009	Alex Iosevich Mischa Rudnev	3
+ PDF Chat	Pairs of Dot Products in Finite Fields and Rings	2017	David Covert Steven Senger	2
+	An anti-Ramsey theorem	1985	László Babai	2
+ PDF Chat	Ergodic methods in additive combinatorics	2007	Bryna Kra	2
+	Frames, graphs and erasures	2005	Bernhard G. Bodmann Vern I. Paulsen	2
+	Direct and converse approximation theorems for the Shepard operator	1991	J. Szabados	2