Steve Butler

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All published works

Action	Title	Year	Authors
+	Coalescing sets preserving cospectrality of graphs arising from block similarity matrices	2024	Sajid Bin Mahamud Steve Butler Hannah Graff Jiah Jin Nick Layman Taylor Luck Noah Owen Angela Yuan
+	Spectral faux trees	2024	Steve Butler Elena D’Avanzo Rachel Heikkinen Joel Jeffries Alyssa Kruczek Harper Niergarth
+ PDF Chat	Coalescing sets preserving cospectrality of graphs arising from block similarity matrices	2024	Sajid Bin Mahamud Steve Butler Hannah Graff Nick Layman Taylor Luck Jiah Jin Noah Owen Angela Yuan
+	Passing Drops and Descents	2024	Cailyn Bass Steve Butler
+ PDF Chat	Spectral properties of the exponential distance matrix	2022	Steve Butler Elizabeth Cooper Aaron Li Kate Lorenzen Zoë Schopick
+ PDF Chat	Hadamard Diagonalizable Graphs of Order at Most 36	2022	Jane Breen Steve Butler Melissa Fuentes Bernard Lidický M. Phillips Alexander W. N. Riasanovksy Sung‐Yell Song Ralihe R. Villagrán Cedar Wiseman Xiaohong Zhang
+	Spectral faux trees	2022	Steve Butler Elena D’Avanzo Rachel Heikkinen Joel Jeffries Alyssa Kruczek Harper Niergarth
+	Complements of coalescing sets	2022	Steve Butler Elena D’Avanzo Rachel Heikkinen Joel Jeffries Alyssa Kruczek Harper Niergarth
+ PDF Chat	Ordered multiplicity inverse eigenvalue problem for graphs on six vertices	2021	John Ahn Christine Alar Beth Bjorkman Steve Butler Joshua Carlson Audrey Goodnight Haley Knox Casandra Monroe Michael C. Wigal
+ PDF Chat	Properties of a q-Analogue of Zero Forcing	2020	Steve Butler Craig Erickson Shaun Fallat H. Tracy Hall Brenda K. Kroschel Jephian C.-H. Lin Bryan L. Shader Nathan Warnberg Boting Yang
+ PDF Chat	Enumerating Parking Completions Using Join and Split	2020	Ayomikun Adeniran Steve Butler Galen Dorpalen‐Barry Pamela E. Harris Cyrus Hettle Qingzhong Liang Jeremy L. Martin Hayan Nam
+	The Mathematical Life of Fan Chung	2020	Steve Butler
+	Counting Tilings by Taking Walks in a Graph	2020	Steve Butler Jason Ekstrand Steven Osborne
+	Hadamard diagonalizable graphs of order at most 36	2020	Jane Breen Steve Butler Melissa Fuentes Bernard Lidický Michael J. Phillips Alexander W. N. Riasanovksy Sung‐Yell Song Ralihe R. Villagrán Cedar Wiseman Xiaohong Zhang
+ PDF Chat	Computing Kemeny's constant for a barbell graph	2019	Jane Breen Steve Butler Nicklas Day Colt DeArmond Kate Lorenzen Haoyang Qian Jacob Riesen
+ PDF Chat	Computing Kemeny's constant for a barbell graph	2019	Jane Breen Steve Butler Nicklas Day Colt DeArmond Kate Lorenzen Haoyang Qian Jacob Riesen
+	A Jaunt in Spectral Graph Theory	2019	Steve Butler
+	The inverse eigenvalue problem of a graph: Multiplicities and minors	2019	Wayne Barrett Steve Butler Shaun Fallat H. Tracy Hall Leslie Hogben Jephian C.-H. Lin Bryan L. Shader Michael E. Young
+ PDF Chat	Graphs with at most two trees in a forest-building process	2019	Steve Butler Misa Hamanaka Marie Hardt
+	Proof Without Words: Independent Sets in Grid graphs and Tilings of Aztec Diamonds	2019	Steve Butler
+ PDF Chat	On the genus of a quotient of a numerical semigroup	2019	Ayomikun Adeniran Steve Butler Colin Defant Yibo Gao Pamela E. Harris Cyrus Hettle Qingzhong Liang Hayan Nam Adam Volk
+	Enumerating Parking Completions Using Join and Split	2019	Ayomikun Adeniran Steve Butler Galen Dorpalen-Barry Pamela E. Harris Cyrus Hettle Qingzhong Liang Jeremy L. Martin Hayan Nam
+	Enumerating Multiplex Juggling Patterns.	2019	Steve Butler Jeongyoon Choi Kimyung Kim Kyuhyeok Seo
+	Spectral properties of the exponential distance matrix	2019	Steve Butler Elizabeth Coper Aaron Li Kate Lorenzen Zoë Schopick
+	Graph switching, 2-ranks, and graphical Hadamard matrices	2018	Aida Abiad Steve Butler Willem H. Haemers
+	Permutations Resilient to Deletions	2018	Noga Alon Steve Butler Ron Graham Utkrisht Rajkumar
+	Graphs with at most two trees in a forest building process.	2018	Steve Butler Misa Hamanaka Marie Hardt
+	Graph switching, 2-ranks, and graphical Hadamard matrices	2018	Aida Abiad Steve Butler Willem H. Haemers
+	Properties of a $q$-analogue of zero forcing	2018	Steve Butler Craig Erickson Shaun Fallat H. Tracy Hall Brenda K. Kroschel Jephian C.-H. Lin Bryan L. Shader Nathan Warnberg Boting Yang
+	Graphs with at most two trees in a forest building process	2018	Steve Butler Misa Hamanaka Marie Hardt
+	A forest building process on simple graphs	2017	Zhanar Berikkyzy Steve Butler Jay Cummings Kristin Heysse Paul Horn Ruth Luo Brent Moran
+	Ordered multiplicity inverse eigenvalue problem for graphs on six vertices	2017	John Ahn Christine Alar Beth Bjorkman Steve Butler Joshua Carlson Audrey Goodnight Haley Knox Casandra Monroe Michael C. Wigal
+	The inverse eigenvalue problem of a graph: Multiplicities and minors	2017	Wayne Barrett Steve Butler Shaun Fallat H. Tracy Hall Leslie Hogben Jephian C.-H. Lin Bryan L. Shader Michael E. Young
+	Parking distributions on trees	2017	Steve Butler Ron Graham Catherine H. Yan
+ PDF Chat	A generalization of Eulerian numbers via rook placements	2017	Esther Banaian Steve Butler Christopher Cox Jeffrey Davis Jacob Landgraf Scarlitte Ponce
+ PDF Chat	The Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices	2017	Steve Butler Minerva Catral H. Tracy Hall Leslie Hogben Xavier Martínez-Rivera Bryan L. Shader P. van den Driessche
+	Enumerating multiplex juggling patterns	2017	Steve Butler Jeongyoon Choi Kimyung Kim Kyuhyeok Seo
+	Juggling card sequences	2017	Steve Butler Fan Chung Jay Cummings Ron Graham
+	Ordered multiplicity inverse eigenvalue problem for graphs on six vertices	2017	John Ahn Christine Alar Beth Bjorkman Steve Butler Joshua M. Carlson Audrey Goodnight Haley Knox Casandra Monroe Michael C. Wigal
+	The inverse eigenvalue problem of a graph: Multiplicities and minors	2017	Wayne Barrett Steve Butler Shaun Fallat H. Tracy Hall Leslie Hogben Jephian C.-H. Lin Bryan L. Shader Michael Young
+	A forest building process on simple graphs	2016	Zhanar Berikkyzy Steve Butler Jay Cummings Kristin Heysse Paul Horn Ruth Luo Brent Moran
+	A cospectral family of graphs for the normalized Laplacian found by toggling	2016	Steve Butler Kristin Heysse
+ PDF Chat	Counting Prime Juggling Patterns	2016	Esther Banaian Steve Butler Christopher Cox Jeffrey Davis Jacob Landgraf Scarlitte Ponce
+ PDF Chat	Rainbow arithmetic progressions	2016	Steve Butler Craig Erickson Leslie Hogben Kirsten Hogenson Lucas Kramer Richard Krämer Jephian C.-H. Lin Ryan R. Martin Derrick Stolee Nathan Warnberg
+	Algebraic aspects of the normalized Laplacian	2016	Steve Butler
+	The Mathematics of the Flip and Horseshoe Shuffles	2016	Steve Butler Persi Diaconis Ron Graham
+	A forest building process on simple graphs	2016	Zhanar Berikkyzy Steve Butler Jay Cummings Kristin Heysse Paul Horn Ruth Luo Brent Moran
+	Rudiments of Ramsey Theory	2015	Ron Graham Steve Butler
+	The theorems of Schur, Folkman, and Hindman	2015	Ron Graham Steve Butler
+	Rado’s theorem	2015	Ron Graham Steve Butler
+	A general Ramsey product theorem	2015	Ron Graham Steve Butler
+	Szemerédi’s theorem	2015	Ron Graham Steve Butler
+	Counting prime juggling patterns	2015	Esther Banaian Steve Butler Christopher Cox Jeffrey Davis Jacob Landgraf Scarlitte Ponce
+	A cospectral family of graphs for the normalized Laplacian found by toggling	2015	Steve Butler Kristin Heysse
+ PDF Chat	Using twins and scaling to construct cospectral graphs for the normalized Laplacian	2015	Steve Butler
+ PDF Chat	The enhanced principal rank characteristic sequence	2015	Steve Butler Minerva Catral Shaun Fallat H. Tracy Hall Leslie Hogben P. van den Driessche Michael E. Young
+	Symmetric 0–1 matrices with inverses having two distinct values and constant diagonal	2015	Wayne Barrett Steve Butler H. Tracy Hall
+	Partition and sum is fast	2015	Steve Butler Ronald Graham Richard Stong
+	Juggling card sequences	2015	Steve Butler Fan Chung Jay Cummings Ron Graham
+	Egyptian Fractions with Each Denominator Having Three Distinct Prime Divisors.	2015	Steve Butler Paul Erdös Ron Graham
+	A cospectral family of graphs for the normalized Laplacian found by toggling	2015	Steve Butler Kristin Heysse
+	Partition and sum is fast	2015	Steve Butler Ron Graham Richard Stong
+	Counting prime juggling patterns	2015	Esther Banaian Steve Butler Christopher Cox Jeffrey A. Davis Jacob Landgraf Scarlitte Ponce
+	Using twins and scaling to construct cospectral graphs for the normalized Laplacian	2014	Steve Butler
+	Rainbow arithmetic progressions	2014	Steve Butler Craig Erickson Leslie Hogben Kirsten Hogenson Lucas Kramer Richard Krämer Jephian C.-H. Lin Ryan R. Martin Derrick Stolee Nathan Warnberg
+ PDF Chat	Unrolling Residues to Avoid Progressions	2014	Steve Butler Ron Graham Linyuan Lü
+ PDF Chat	Tiling a Strip with Triangles	2014	John Bodeen Steve Butler Taekyoung Kim Xiyuan Sun Shenzhi Wang
+	The mathematics of the flip and horseshoe shuffles	2014	Steve Butler Persi Diaconis Ron Graham
+	De Bruijn Sequences with Varying Combs.	2014	Abbas Alhakim Steve Butler Ron Graham
+	Using twins and scaling to construct cospectral graphs for the normalized Laplacian	2014	Steve Butler
+	Rainbow arithmetic progressions	2014	Steve Butler Craig A. Erickson Leslie Hogben Kirsten Hogenson Lucas Kramer Richard Krämer Jephian C.-H. Lin Ryan R. Martin Derrick Stolee Nathan Warnberg
+	Spectral Graph Theory	2013	Steve Butler Fan Chung
+	An interstice relationship for flowers with four petals	2013	Steve Butler Ron Graham Gerhard Guettler Colin L. Mallows
+ PDF Chat	CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION	2013	Steve Butler Erik D. Demaine RON GRAHAM Tomohiro Tachi
+	The Mathematics of Paul Erdős II	2013	Ronald Graham Jaroslav Nešetřil Steve Butler
+	Subdivision Using Angle Bisectors Is Dense in the Space of Triangles	2013	Steve Butler Ron Graham
+	Zero forcing for inertia sets	2012	Steve Butler Jason Grout H. Tracy Hall
+	Unrolling residues to avoid progressions	2012	Steve Butler Ron Graham Linyuan Lü
+ PDF Chat	A Construction of Cospectral Graphs for the Normalized Laplacian	2011	Steve Butler Jason Grout
+	Hypercube orientations with only two in-degrees	2011	Joe Buhler Steve Butler Ron Graham Eric Tressler
+	Origami rings	2010	Joe Buhler Steve Butler Warwick de Launey Ron Graham
+	A construction of cospectral graphs for the normalized Laplacian	2010	Steve Butler Jason Grout
+	A new proof for a modular condition of Lucas numbers	2010	Steve Butler
+	Shuffling with ordered cards	2010	Steve Butler Ron Graham
+ PDF Chat	Tiling Polygons with Lattice Triangles	2010	Steve Butler Fan Chung Ron Graham Miklós Laczkovich
+ PDF Chat	Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian	2010	Steve Butler Fan Chung
+ PDF Chat	Enumerating (Multiplex) Juggling Sequences	2010	Steve Butler Ron Graham
+	Subdivision by bisectors is dense in the space of all triangles	2010	Steve Butler Ron Graham
+	The art of juggling with two balls or A proof for a modular condition of Lucas numbers	2010	Steve Butler
+ PDF Chat	Finding Patterns Avoiding Many Monochromatic Constellations	2010	Steve Butler Kevin Costello Ron Graham
+	A Note on Nested Sums	2010	Steve Butler Pavel Karasik
+	Shuffling with ordered cards	2010	Steve Butler Ron Graham
+	A construction of cospectral graphs for the normalized Laplacian	2010	Steve Butler Jason Grout
+	Hypercube orientations with only two in-degrees	2010	Joe Buhler Steve Butler Ron Graham Eric Tressler
+	Origami rings	2010	Joe Buhler Steve Butler Warwick de Launey Ron Graham
+	Iterated Triangle Partitions	2010	Steve Butler Ron Graham
+	Induced-Universal Graphs for Graphs with Bounded Maximum Degree	2009	Steve Butler
+	Eigenvalues of 2-edge-coverings	2009	Steve Butler
+ PDF Chat	Irreducible Apollonian Configurations and Packings	2009	Steve Butler Ron Graham Gerhard Guettler Colin L. Mallows
+	A note about cospectral graphs for the adjacency and normalized Laplacian matrices	2009	Steve Butler
+	Jumping sequences	2008	Steve Butler Ron Graham Nan Zang
+	Hat Guessing Games	2008	Steve Butler Mohammad Taghi Hajiaghayi Robert Kleinberg Tom Leighton
+	Enumerating (multiplex) juggling sequences	2008	Steve Butler Ron Graham
+	Jumping sequences	2008	Steve Butler Ron Graham Nan Zang
+ PDF Chat	Forest-Like Permutations	2007	Mireille Bousquet‐Mélou Steve Butler
+ PDF Chat	Interlacing for weighted graphs using the normalized Laplacian	2007	Steve Butler
+	Using discrepancy to control singular values for nonnegative matrices	2006	Steve Butler
+ PDF Chat	Recurrent Events Analysis in the Presence of Time-Dependent Covariates and Dependent Censoring	2003	Maja Miloslavsky Sündüz Keleş Mark J. van der Laan Steve Butler

Common Coauthors

Coauthor	Papers Together
Ron Graham	33
Leslie Hogben	8
H. Tracy Hall	8
Jephian C.-H. Lin	8
Bryan L. Shader	6
Kristin Heysse	6
Shaun Fallat	6
Jay Cummings	5
Fan Chung	5
Michael E. Young	5
Nathan Warnberg	5
Joe Buhler	4
Jane Breen	4
Jason Grout	4
Scarlitte Ponce	4
Jacob Landgraf	4
Kate Lorenzen	4
Esther Banaian	4
Wayne Barrett	4
Craig Erickson	4
Jeffrey Davis	3
Audrey Goodnight	3
Haley Knox	3
Ayomikun Adeniran	3
Marie Hardt	3
Richard Krämer	3
Elena D’Avanzo	3
Beth Bjorkman	3
Joel Jeffries	3
Harper Niergarth	3
Misa Hamanaka	3
Derrick Stolee	3
Lucas Kramer	3
Ruth Luo	3
Kirsten Hogenson	3
Zhanar Berikkyzy	3
Qingzhong Liang	3
Christopher Cox	3
Cyrus Hettle	3
Casandra Monroe	3
Pamela E. Harris	3
Alyssa Kruczek	3
Michael C. Wigal	3
Christine Alar	3
Brent Moran	3
Ryan R. Martin	3
Rachel Heikkinen	3
Hayan Nam	3
Melissa Fuentes	2
Nan Zang	2

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Spectral Graph Theory	1996	Fan Chung	8
+	Juggling Drops and Descents	1994	Joe Buhler David Eisenbud Ron Graham Colin Wright	6
+ PDF Chat	Which graphs are determined by their spectrum?	2003	Edwin van Dam Willem H. Haemers	5
+	THE NORMALIZED LAPLACIAN MATRIX AND GENERAL RANDI C INDEX OF GRAPHS	2010	Michael Cavers	5
+	Spectra of Graphs	2011	Andries E. Brouwer Willem H. Haemers	5
+ PDF Chat	Primitive Juggling Sequences	2008	Fan Chung Ron Graham	5
+ PDF Chat	Zero forcing parameters and minimum rank problems	2010	Francesco Barioli Wayne Barrett Shaun Fallat H. Tracy Hall Leslie Hogben Bryan L. Shader P. van den Driessche Hein van der Holst	5
+ PDF Chat	A Construction of Cospectral Graphs for the Normalized Laplacian	2011	Steve Butler Jason Grout	5
+ PDF Chat	The On-Line Encyclopedia of Integer Sequences	2007	N. J. A. Sloane	5
+ PDF Chat	Using twins and scaling to construct cospectral graphs for the normalized Laplacian	2015	Steve Butler	4
+ PDF Chat	Enumerating (Multiplex) Juggling Sequences	2010	Steve Butler Ron Graham	4
+ PDF Chat	Spectral graph theory and the inverse eigenvalue problem of a graph	2005	Leslie Hogben	4
+	Juggling and applications to q-analogues	1996	Richard Ehrenborg Margaret Readdy	3
+	A new proof of Szemerédi's theorem	2001	W. T. Gowers	3
+	The Sequence of Pedal Triangles	1988	J. G. Kingston J. L. Synge	3
+	Eigenvalues of 2-edge-coverings	2009	Steve Butler	3
+	Generalized barycentric subdivision of a triangle and semigroups of Mobius transformations	2000	Андрей Александрович Ордин	3
+ PDF Chat	Noncommuting random products	1963	Harry Furstenberg	3
+ PDF Chat	Iterated random functions	2017	Persi Diaconis David A. Freedman	3
+	On the eigenvalues of generalized and double generalized stars	2005	Francesco Barioli Shaun Fallat	3
+	Juggling card sequences	2015	Steve Butler Fan Chung Jay Cummings Ron Graham	3
+	The Ergodic Character of Sequences of Pedal Triangles	1990	Peter D. Lax	3
+	Constructing cospectral graphs	1982	Chris Godsil Brendan D. McKay	3
+	Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph	2017	Wayne Barrett Shaun Fallat H. Tracy Hall Leslie Hogben Jephian C.-H. Lin Bryan L. Shader	3
+	On the asymptotic minimum number of monochromatic 3-term arithmetic progressions	2007	Pablo A. Parrilo Aaron Robertson Dan Saracino	3
+ PDF Chat	Barycentric subdivision of triangles and semigroups of Möbius maps	1996	Imre Bárány Alan F. Beardon T. K. Carne	3
+	The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample	2009	Wayne Barrett H. Tracy Hall Raphael Loewy	3
+ PDF Chat	Coverings, Heat Kernels and Spanning Trees	1998	Fan Chung Shing‐Tung Yau	2
+	Spectra of graphs : theory and application	1995	Dragoš Cvetković Michael Doob H. Sachs	2
+	Quantitative theorems for regular systems of equations	1988	Péter Frankl Ronald Graham V. Rödl	2
+	Combinatorics of Set Partitions	2012	Toufik Mansour	2
+ PDF Chat	None	1992	Noam Elkies Greg Kuperberg Michael Larsen James Propp	2
+ PDF Chat	Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings	2005	Ronald Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan	2
+ PDF Chat	On Rainbow Arithmetic Progressions	2004	Maria Axenovich D. Fon-Der-Flaass	2
+	None	1999	Miklós Bóna	2
+ PDF Chat	Enumeration of cospectral graphs	2003	Willem H. Haemers Edward Spence	2
+ PDF Chat	Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions	2005	Ronald Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan	2
+	A note on the binomial drop polynomial of a poset	1994	Joe Buhler Ron Graham	2
+ PDF Chat	None	1992	Noam D. Elkies Greg Kuperberg Michael Larsen James Propp	2
+	On Sets of Integers Which Contain No Three Terms in Arithmetical Progression	1946	Felix Behrend	2
+	On the second eigenvalue of random regular graphs	1989	Joel Friedman J. Kahn Endre Szemerédi	2
+	On Character Sums and Primitive Roots<sup>†</sup>	1962	D. A. Burgess	2
+	Generalized Parking Functions, Tree Inversions, and Multicolored Graphs	2001	Catherine H. Yan	2
+ PDF Chat	Cospectral Graphs on 12 Vertices	2009	A.E. Brouwer Euan A. Spence	2
+	On sets of integers not containing long arithmetic progressions	2001	Izabella Łaba Michael T. Lacey	2
+ PDF Chat	Rational Parking Functions and Catalan Numbers	2015	Drew Armstrong Nicholas A. Loehr Gregory S. Warrington	2
+	A note about cospectral graphs for the adjacency and normalized Laplacian matrices	2009	Steve Butler	2
+ PDF Chat	A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron	2002	Richard P. Stanley Jim Pitman	2
+	Universal graphs and induced‐universal graphs	1990	Fan Chung	2
+	Rainbow Arithmetic Progressions and Anti-Ramsey Results	2003	Veselin Jungić Jonathan D. Licht Mohammad Mahdian Jaroslav Nešetřil Radoš Radoičić	2