Louis W. Shapiro

Generating author description...

All published works

Action	Title	Year	Authors
+	Combinatorial Reciprocity for Riordan Arrays	2025	Jihyeug Jang Louis W. Shapiro Minho Song
+	A Riordan group poset	2024	Louis W. Shapiro Minho Song
+	An invitation to the Riordan group	2023	Dennis Davenport Shakuan Frankson Louis W. Shapiro Leon C. Woodson
+ PDF Chat	Combinatorial Sums and Inversions	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	The Riordan Group and Applications	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Extensions of the Riordan Group	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Introduction	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Characterization of Riordan Arrays by Special Sequences	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Extraction of Coefficients and Generating Functions	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	The Riordan Group	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Orthogonal Polynomials	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	q-Analogs of Riordan Arrays	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Generalized Riordan Arrays	2022	Louis W. Shapiro Renzo Sprugnoli Paul Barry Gi‐Sang Cheon Tian-Xiao He Donatella Merlini Weiping Wang
+	Pseudo-involutions in the Riordan group	2021	Alexander Burstein Louis W. Shapiro
+	Palindromes and pseudo-involution multiplication	2020	Tian-Xiao He Louis W. Shapiro
+	A Bijection Between the Triangulations of Convex Polygons and Ordered Trees.	2020	Dennis Davenport Louis W. Shapiro Leon C. Woodson
+	Fuss–Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group	2017	Tian-Xiao He Louis W. Shapiro
+	Constructing Pseudo-Involutions in the Riordan Group.	2017	Dev Phulara Louis W. Shapiro
+	Profiles of ordered trees with mutation and associated Riordan matrices	2016	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	Row sums and alternating sums of Riordan arrays	2016	Tian-Xiao He Louis W. Shapiro
+	A combinatorial equivalence relation for formal power series	2015	Gi‐Sang Cheon Sung-Tae Jin Louis W. Shapiro
+	The Boundary of Ordered Trees.	2015	Dennis Davenport Louis W. Shapiro Lara Pudwell Leon C. Woodson
+	Mutation effects in ordered trees	2014	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	Generalized Bessel numbers and some combinatorial settings	2013	Gi‐Sang Cheon Ji-Hwan Jung Louis W. Shapiro
+	Combinatorics of Riordan arrays with identical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.gif" display="inline" overflow="scroll"><mml:mi>A</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi></mml:math> sequences	2012	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+ PDF Chat	The Double Riordan Group	2012	Dennis Davenport Louis W. Shapiro Leon C. Woodson
+	The uplift principle for ordered trees	2011	Gi‐Sang Cheon Louis W. Shapiro
+	Fuss-Catalan Matrices and Their Weighted Sums	2011	Tian-Xiao He Louis W. Shapiro
+	The hitting time subgroup, Łukasiewicz paths and Faber polynomials	2010	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	An algebraic structure for Faber polynomials	2010	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees	2010	William Y. C. Chen Louis W. Shapiro Susan Y. J. Wu
+	The Fine numbers refined	2009	Gi‐Sang Cheon Sang‐Gu Lee Louis W. Shapiro
+	Riordan group involutions and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si38.gif" display="inline" overflow="scroll"><mml:mi>Δ</mml:mi></mml:math>-sequence	2009	Gi‐Sang Cheon Sung-Tae Jin Hana Kim Louis W. Shapiro
+	The Riordan Group and Symmetric Lattice Paths	2009	Deng Li-hua Eva Y. P. Deng Louis W. Shapiro
+	A Bijection Between 3-Motzkin Paths and Schroder Paths With No Peak at Odd Height	2009	Louis W. Shapiro Carol J. Wang
+	A generalization of Lucas polynomial sequence	2008	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	Riordan group involutions	2007	Gi‐Sang Cheon Hana Kim Louis W. Shapiro
+	Protected points in ordered trees	2007	Gi‐Sang Cheon Louis W. Shapiro
+	The butterfly decomposition of plane trees	2007	William Y. C. Chen Nelson Y. Li Louis W. Shapiro
+	On Sequences G n Satisfying G n = (d + 2)G n 1 G n 2	2007	Ricky X. F. Chen Louis W. Shapiro
+	Matrix identities on weighted partial Motzkin paths	2006	William Y. C. Chen Nelson Y. Li Louis W. Shapiro Sherry H. F. Yan
+	Pell Walks and Riordan Matrices	2005	Asamoah Nkwanta Louis W. Shapiro
+ PDF Chat	Parity reversing involutions on plane trees and 2-Motzkin paths	2005	William Y. C. Chen Louis W. Shapiro Laura L. M. Yang
+	Matrix Identities on Weighted Partial Motzkin Paths	2005	William Y. C. Chen Nelson Y. Li Louis W. Shapiro Sherry H. F. Yan
+	Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths	2005	William Y. C. Chen Louis W. Shapiro Laura L. M. Yang
+	The Butterfly Decomposition of Plane Trees	2005	William Y. C. Chen Nelson Y. Li Louis W. Shapiro
+	Bijections and the Riordan group	2003	Louis W. Shapiro
+	A bijection between ordered trees and 2-Motzkin paths and its many consequences	2002	Emeric Deutsch Louis W. Shapiro
+	A survey of the Fine numbers	2001	Emeric Deutsch Louis W. Shapiro
+	Bijections for the Schröder Numbers	2000	Louis W. Shapiro Robert A. Sulanke
+	Bijections for the Schröder Numbers	2000	Louis W. Shapiro Robert A. Sulanke
+	Characterization of Some Character Degrees: 10458	1998	Frank Schmidt Louis W. Shapiro Stephen M. Gagola Bertram Huppert
+	Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths	1993	Joseph E. Bonin Louis W. Shapiro Rodica Simion
+	How to Guess a Generating Function	1992	Seyoum Getu Louis W. Shapiro Wen-Jin Woan Leon C. Woodson
+	Random walks with absorbing points	1992	Louis W. Shapiro
+	Bootstrap Percolation, the Schröder Numbers, and the<i>N</i>-Kings Problem	1991	Louis W. Shapiro A. B. Stephens
+	Voting blocks, reluctant functions, and a formula of Hurwitz	1991	Louis W. Shapiro
+	An Electrical Lemma	1987	Louis W. Shapiro
+	A lattice path lemma and an application in enzyme kinetics	1986	Louis W. Shapiro
+ PDF Chat	Positive Definite Matrices and Catalan Numbers, Revisited	1984	Louis W. Shapiro
+ PDF Chat	Positive definite matrices and Catalan numbers, revisited	1984	Louis W. Shapiro
+	Runs, Slides and Moments	1983	Louis W. Shapiro Wen-Jin Woan Seyoum Getu
+	A combinatorial proof of a Chevyshev polynomial identity	1981	Louis W. Shapiro
+	A combinatorial proof of a Chevyshev polynomial identity	1981	Louis W. Shapiro
+	Deques, trees and lattice paths	1981	Douglas G. Rogers Louis W. Shapiro
+	Some correspondences involving the schröder numbers and relations	1978	Douglas G. Rogers Louis W. Shapiro
+	Motzkin numbers	1977	Robert Donaghey Louis W. Shapiro
+	Fibonacci Numbers and Upper Triangular Groups	1976	Louis W. Shapiro
+	A short proof of an identity of Touchard's concerning catalan numbers	1976	Louis W. Shapiro
+	A Catalan triangle	1976	Louis W. Shapiro
+	Upper Triangular Rings, Ideals, and Catalan Numbers	1975	Louis W. Shapiro
+	Finite Groups Acting on Sets with Applications	1973	Louis W. Shapiro
+	Finite Groups Acting on Sets with Applications	1973	Louis W. Shapiro
+	Group representations and algebraic number fields	1969	Louis W. Shapiro

Common Coauthors

Coauthor	Papers Together
Gi‐Sang Cheon	23
Tian-Xiao He	14
Renzo Sprugnoli	10
Donatella Merlini	10
Paul Barry	10
Weiping Wang	10
William Y. C. Chen	7
Hana Kim	6
Leon C. Woodson	5
Nelson Y. Li	4
Dennis Davenport	4
Seyoum Getu	2
Minho Song	2
Sung-Tae Jin	2
Hana Kim	2
Robert A. Sulanke	2
Emeric Deutsch	2
Laura L. M. Yang	2
Wen-Jin Woan	2
Douglas G. Rogers	2
Sherry H. F. Yan	2
Asamoah Nkwanta	1
Sang‐Gu Lee	1
A. B. Stephens	1
Lara Pudwell	1
Carol J. Wang	1
Stephen M. Gagola	1
Rodica Simion	1
Ricky X. F. Chen	1
Ji-Hwan Jung	1
Dev Phulara	1
Joseph E. Bonin	1
Robert Donaghey	1
Bertram Huppert	1
Eva Y. P. Deng	1
Jihyeug Jang	1
Alexander Burstein	1
Susan Y. J. Wu	1
Shakuan Frankson	1
Deng Li-hua	1
Frank Schmidt	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Riordan arrays and combinatorial sums	1994	Renzo Sprugnoli	20
+	Advanced Combinatorics	1974	Louis Comtet	15
+ PDF Chat	On Some Alternative Characterizations of Riordan Arrays	1997	Donatella Merlini Douglas G. Rogers Renzo Sprugnoli M. Cecilia Verri	13
+ PDF Chat	The On-Line Encyclopedia of Integer Sequences	2007	N. J. A. Sloane	12
+	Bijections and the Riordan group	2003	Louis W. Shapiro	11
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	11
+	Sequence characterization of Riordan arrays	2008	Tian-Xiao He Renzo Sprugnoli	9
+	A bijection between ordered trees and 2-Motzkin paths and its many consequences	2002	Emeric Deutsch Louis W. Shapiro	8
+	A survey of the Fine numbers	2001	Emeric Deutsch Louis W. Shapiro	8
+	Combinatorial Enumeration	2024	Robin Pemantle Mark C. Wilson Stephen Melczer	7
+	A divisibility property for a subgroup of Riordan matrices	2000	Paul Peart Wen-Jin Woan	6
+ PDF Chat	The enumeration of tree-like polyhexes	1970	Frank Harary Ronald C. Read	6
+	Production matrices	2004	Emeric Deutsch Luca Ferrari Simone Rinaldi	5
+	Dyck path enumeration	1999	Emeric Deutsch	5
+ PDF Chat	Production Matrices and Riordan Arrays	2009	Emeric Deutsch Luca Ferrari Simone Rinaldi	5
+	Riordan arrays and the Abel-Gould identity	1995	Renzo Sprugnoli	5
+	Identities induced by Riordan arrays	2011	Ana Luzón Donatella Merlini Manuel A. Morón Renzo Sprugnoli	5
+	A Catalan triangle	1976	Louis W. Shapiro	5
+	Asymptotic Methods in Enumeration	1974	Edward A. Bender	5
+	Generalized Riordan arrays	2008	Weiping Wang Tianming Wang	5
+	The Sheffer group and the Riordan group	2007	Tian-Xiao He L. C. Hsu Peter J.-S. Shiue	5
+	Motzkin numbers	1977	Robert Donaghey Louis W. Shapiro	4
+	Motzkin Numbers	1998	Martin Aigner	4
+	Matrix characterizations of Riordan arrays	2014	Tian-Xiao He	4
+	Twelve Countings with Rooted Plane Trees	1997	Martin Klazar	4
+	Combinatorics of Riordan arrays with identical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.gif" display="inline" overflow="scroll"><mml:mi>A</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.gif" display="inline" overflow="scroll"><mml:mi>Z</mml:mi></mml:math> sequences	2012	Gi‐Sang Cheon Hana Kim Louis W. Shapiro	4
+ PDF Chat	Combinatorial Theory Seminar Eindhoven University of Technology	1974	J. H. van Lint	4
+	Protected points in ordered trees	2007	Gi‐Sang Cheon Louis W. Shapiro	3
+	Analytic Combinatorics	2009	Philippe Flajolet Robert Sedgewick	3
+	A Course in Enumeration	2007	Martin Aigner	3
+	Constructing Pseudo-Involutions in the Riordan Group.	2017	Dev Phulara Louis W. Shapiro	3
+	Generating Functions via Hankel and Stieltjes Matrices	2000	Paul Peart Wen-Jin Woan	3
+	A schröder triangle: Three combinatorial problems	1977	Douglas G. Rogers	3
+	q-Catalan numbers	1985	J Fürlinger Josef Hofbauer	3
+	Enumerative Combinatorics	1999	Richard P. Stanley Sergey Fomin	3
+	Some Open Questions about Random Walks, Involutions, Limiting Distributions, and Generating Functions	2001	Lou Shapiro	3
+	Trees Associated with the Motzkin Numbers	1996	Alexander Kuznetsov Igor Pak Alexander Postnikov	3
+	Sur les partitions non croisees d'un cycle	1972	G. Kreweras	3
+	Enumeration of plane trees by branches and endpoints	1975	John Riordan	3
+	Combinatorial aspects of continued fractions	1980	Philippe Flajolet	3
+	Some correspondences involving the schröder numbers and relations	1978	Douglas G. Rogers Louis W. Shapiro	3
+	Deques, trees and lattice paths	1981	Douglas G. Rogers Louis W. Shapiro	3
+	Structural properties of Riordan matrices and extending the matrices	2011	Gi‐Sang Cheon Sung-Tae Jin	3
+	Some algebraic structure of the Riordan group	2012	Candice Angel Jean-Louis Asamoah Nkwanta	3
+	Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths	1993	Joseph E. Bonin Louis W. Shapiro Rodica Simion	3
+	The Cauchy numbers	2006	Donatella Merlini Renzo Sprugnoli M. Cecilia Verri	3
+ PDF Chat	Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products	1948	Th. Motzkin	3
+	The uplift principle for ordered trees	2011	Gi‐Sang Cheon Louis W. Shapiro	3
+	Lagrange Inversion: When and How	2006	Donatella Merlini Rachele Sprugnoli M. Cecilia Verri	3
+	On the Partitions of a Polygon	1890	Cayley	3