@book{stanley_enumerative_1999,
	location = {Cambridge},
	title = {Enumerative combinatorics. Vol. 2},
	volume = {62},
	isbn = {0-521-56069-1 0-521-78987-7},
	series = {Cambridge Studies in Advanced Mathematics},
	pagetotal = {xii+581},
	publisher = {Cambridge University Press},
	author = {Stanley, Richard P.},
	date = {1999},
	doi = {10.1017/CBO9780511609589}
}

@misc{sloane_-line_nodate,
	title = {The On-Line Encyclopedia of Integer Sequences},
	url = {http://oeis.org},
	author = {Sloane, Neil J. A.}
}

@article{elizalde_fixed_2012,
	title = {Fixed Points and Excedances in Restricted Permutations},
	volume = {18},
	rights = {Copyright (c)},
	issn = {1077-8926},
	url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i2p29},
	pages = {29},
	number = {2},
	journaltitle = {The Electronic Journal of Combinatorics},
	author = {Elizalde, Sergi},
	date = {2012-01-02},
	langid = {american},
	file = {Full Text PDF:/Users/sergi/Zotero/storage/PDRNBTC3/Elizalde - 2012 - Fixed Points and Excedances in Restricted Permutat.pdf:application/pdf;Snapshot:/Users/sergi/Zotero/storage/I6DMZLVH/pdf.html:text/html}
}

@article{deutsch_statistics_2017,
	title = {Statistics on bargraphs viewed as cornerless Motzkin paths},
	volume = {221},
	issn = {0166-218X},
	doi = {10.1016/j.dam.2016.12.026},
	abstract = {A bargraph is a self-avoiding lattice path with steps U=(0,1), H=(1,0) and D=(0,?1) that starts at the origin and ends on the x-axis, and stays strictly above the x-axis everywhere except at the endpoints. Bargraphs have been studied as a special class of convex polyominoes, and enumerated using the so-called wasp-waist decomposition of Bousquet-M\'elou and Rechnitzer. In this paper we note that there is a trivial bijection between bargraphs and Motzkin paths without peaks or valleys. This allows us to use the recursive structure of Motzkin paths to enumerate bargraphs with respect to several statistics, finding simpler derivations of known results and obtaining many new ones. We also count symmetric bargraphs and alternating bargraphs. In some cases we construct statistic-preserving bijections between different combinatorial objects, proving some identities that we encounter along the way.},
	pages = {54--66},
	journaltitle = {Discrete Applied Mathematics},
	author = {Deutsch, Emeric and Elizalde, Sergi},
	date = {2017-04-20},
	keywords = {Bargraph, Bijection, Motzkin path, Statistic},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/65UBPG2J/Deutsch and Elizalde - 2017 - Statistics on bargraphs viewed as cornerless Motzk.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/X7WU7YVT/S0166218X17300057.html:text/html}
}

@article{barnabei_descent_2014,
	title = {Descent sets on 321-avoiding involutions and hook decompositions of partitions},
	volume = {128},
	issn = {0097-3165},
	doi = {10.1016/j.jcta.2014.08.002},
	abstract = {We show that the distribution of the major index over the set of involutions in Sn that avoid the pattern 321 is given by the q-analogue of the n-th central binomial coefficient. The proof consists of a composition of three non-trivial bijections, one being the Robinson–Schensted correspondence, ultimately mapping those involutions with major index m into partitions of m whose Young diagram fits inside a ?n2?×?n2? box. We also obtain a refinement that keeps track of the descent set, and we deduce an analogous result for the comajor index of 123-avoiding involutions.},
	pages = {132--148},
	journaltitle = {Journal of Combinatorial Theory, Series A},
	author = {Barnabei, Marilena and Bonetti, Flavio and Elizalde, Sergi and Silimbani, Matteo},
	date = {2014-11-01},
	keywords = {Descent, Integer partition, Lattice path, Major index, Restricted involution},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/Y4EXUIIS/Barnabei et al. - 2014 - Descent sets on 321-avoiding involutions and hook .pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/EXK9P2BF/S0097316514001010.html:text/html}
}

@article{elizalde_bijections_2015,
	title = {Bijections for pairs of non-crossing lattice paths and walks in the plane},
	volume = {49},
	issn = {0195-6698},
	doi = {10.1016/j.ejc.2015.02.028},
	abstract = {It is a classical result in combinatorics that among lattice paths with 2m steps U=(1,1) and D=(1,?1) starting at the origin, the number of those that do not go below the x-axis equals the number of those that end on the x-axis. A much more unfamiliar fact is that the analogous equality obtained by replacing single paths with k-tuples of non-crossing paths holds for every k. This result has appeared in the literature in different contexts involving plane partitions (where it was proved by Proctor), partially ordered sets, Young tableaux, and lattice walks, but no bijective proof for k?2 seems to be known. In this paper we give a bijective proof of the equality for k=2, showing that for pairs of non-crossing lattice paths with 2m steps U and D, the number of those that do not go below the x-axis equals the number of those that end on the x-axis. Translated in terms of walks in the plane starting at the origin with 2m unit steps in the four coordinate directions, our work provides correspondences among those constrained to the first octant, those constrained to the first quadrant that end on the x-axis, and those in the upper half-plane that end at the origin. Our bijections, which are defined in more generality, also prove new results where different endpoints are allowed, and they give a bijective proof of the formula for the number of walks in the first octant that end on the diagonal, partially answering a question of Bousquet-M\'elou and Mishna.},
	pages = {25--41},
	journaltitle = {European Journal of Combinatorics},
	author = {Elizalde, Sergi},
	date = {2015-10-01},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/C8R5JJKV/Elizalde - 2015 - Bijections for pairs of non-crossing lattice paths.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/VAWCXU77/S0195669815000505.html:text/html}
}

@article{delest_algebraic_1984,
	title = {Algebraic languages and polyominoes enumeration},
	volume = {34},
	issn = {0304-3975},
	doi = {10.1016/0304-3975(84)90116-6},
	abstract = {In this paper, the use of algebraic languages theory in solving an open problem in combinatorics is shown. By constructing a bijection between convex polyominoes and words of an algebraic language, and by solving the corresponding algebraic system, we prove that the number of convex polyominoes with perimeter 2n + 8 is (2n + 11)4n ?4(2n + 1)(2nn).},
	pages = {169--206},
	number = {1},
	journaltitle = {Theoretical Computer Science},
	author = {Delest, Marie-Pierre and Viennot, G\'erard},
	date = {1984-01-01},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/PET693EF/Delest and Viennot - 1984 - Algebraic languages and polyominoes enumeration.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/99N3QALS/0304397584901166.html:text/html}
}

@book{stanley_enumerative_1997,
	location = {Cambridge},
	title = {Enumerative combinatorics. Vol. 1},
	volume = {49},
	isbn = {0-521-55309-1 0-521-66351-2},
	series = {Cambridge Studies in Advanced Mathematics},
	pagetotal = {xii+325},
	publisher = {Cambridge University Press},
	author = {Stanley, Richard P.},
	date = {1997}
}

@book{lladser_walks_2010,
	location = {Providence, Rhode Island},
	title = {Walks with small steps in the quarter plane},
	volume = {520},
	isbn = {978-0-8218-4783-1 978-0-8218-8199-6},
	abstract = {Let S ? \{?1, 0, 1\}2 {\textbackslash} \{(0, 0)\}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and remain in the ?rst quadrant \{(i, j) : i 0, j 0\}. A priori, there are 28 models of this type, but some are trivial. Some others are equivalent to models of walks con?ned to a half-plane, and can therefore be treated systematically using the kernel method, which leads to a generating function that is algebraic.},
	pages = {1--39},
	booktitle = {Contemporary Mathematics},
	publisher = {American Mathematical Society},
	author = {Bousquet-M\'elou, Mireille and Mishna, Marni},
	editor = {Lladser, Manuel E. and Maier, Robert S. and Mishna, Marni and Rechnitzer, Andrew},
	date = {2010},
	langid = {english},
	doi = {10.1090/conm/520/10252},
	file = {Bousquet-M\'elou and Mishna - 2010 - Walks with small steps in the quarter plane.pdf:/Users/sergi/Zotero/storage/X4UF7UFX/Bousquet-M\'elou and Mishna - 2010 - Walks with small steps in the quarter plane.pdf:application/pdf}
}

@article{bousquet-melou_site-perimeter_2003,
	title = {The site-perimeter of bargraphs},
	volume = {31},
	issn = {0196-8858},
	doi = {10.1016/S0196-8858(02)00553-5},
	abstract = {The site-perimeter enumeration of polyominoes that are both column- and row-convex is a well understood problem that always yields algebraic generating functions. Counting more general families of polyominoes is a far more difficult problem. Here we enumerate (by their site-perimeter) the simplest family of polyominoes that are not fully convex—bargraphs. The generating function we obtain is of a type that, to our knowledge, has never been encountered so far in the combinatorics literature: a q-series into which an algebraic series has been substituted.},
	pages = {86--112},
	number = {1},
	journaltitle = {Advances in Applied Mathematics},
	author = {Bousquet-M\'elou, Mireille and Rechnitzer, Andrew},
	date = {2003-07-01},
	langid = {english},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/FPN4VSU5/Bousquet-M\'elou and Rechnitzer - 2003 - The site-perimeter of bargraphs.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/JJP32EV9/S0196885802005535.html:text/html}
}

@article{deng_riordan_2015,
	title = {The Riordan group and symmetric lattice paths},
	volume = {50},
	issn = {1671-9352},
	url = {https://mathscinet.ams.org/mathscinet-getitem?mr=3379160},
	pages = {82--89, 94},
	number = {4},
	journaltitle = {J. Shandong Univ. Nat. Sci.},
	author = {Deng, Li Hua and Deng, Yu Ping and Shapiro, Louis W.},
	date = {2015},
	mrnumber = {3379160},
	file = {MathSciNet Snapshot:/Users/sergi/Zotero/storage/39AUJB23/publdoc.html:text/html}
}

@article{deutsch_bijection_2018,
	title = {A bijection between bargraphs and Dyck paths},
	volume = {251},
	issn = {0166-218X},
	doi = {10.1016/j.dam.2018.04.018},
	abstract = {Bargraphs are a special class of column-convex polyominoes. They can be identified with lattice paths with unit steps north, east, and south that start at the origin, end on the x-axis, and stay strictly above the x-axis everywhere except at the endpoints. Bargraphs, which are used to represent histograms and to model polymers in statistical physics, have been enumerated in the literature by semiperimeter and by several other statistics, using different methods such as the wasp-waist decomposition of Fereti?, and a bijection with certain Motzkin paths. In this paper we describe an unusual bijection between bargraphs and Dyck paths, and study how some statistics are mapped by the bijection. As a consequence, we obtain a new interpretation of Catalan numbers, as counting bargraphs where the semiperimeter minus the number of peaks is fixed.},
	pages = {340--344},
	journaltitle = {Discrete Applied Mathematics},
	author = {Deutsch, Emeric and Elizalde, Sergi},
	date = {2018-12-31},
	langid = {english},
	keywords = {Bargraph, Bijection, Catalan number, Dyck path},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/9U5WUT2C/Deutsch and Elizalde - 2018 - A bijection between bargraphs and Dyck paths.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/56QHPH68/S0166218X18302385.html:text/html}
}

@article{elizalde_bijections_2004,
	title = {Bijections for refined restricted permutations},
	volume = {105},
	issn = {0097-3165},
	doi = {10.1016/j.jcta.2003.10.009},
	abstract = {We present a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson et al. (Ann. Combin. 6 (2003) 427), and Elizalde (Proc. {FPSAC} 2003). We also show that our bijection preserves additional statistics, which extends the previous results.},
	pages = {207--219},
	number = {2},
	journaltitle = {Journal of Combinatorial Theory, Series A},
	author = {Elizalde, Sergi and Pak, Igor},
	date = {2004-02-01},
	langid = {english},
	keywords = {Bijection, Pattern avoidance, Permutaion statistics, Restricted permutations},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/5ZDG4K94/Elizalde and Pak - 2004 - Bijections for refined restricted permutations.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/K93JZRQM/S0097316503001845.html:text/html}
}

@article{feretic_perimeter_2007,
	title = {A perimeter enumeration of column-convex polyominoes},
	volume = {9},
	url = {https://mathscinet.ams.org/mathscinet-getitem?mr=2318442},
	pages = {57--83},
	number = {1},
	journaltitle = {Discrete Math. Theor. Comput. Sci.},
	author = {Fereti?, Svjetlan},
	date = {2007},
	mrnumber = {2318442},
	file = {MathSciNet Snapshot:/Users/sergi/Zotero/storage/G7QVDNII/publdoc.html:text/html}
}

@book{gouyou-beauchamps_chemins_1986,
	location = {Berlin, Heidelberg},
	title = {Chemins sous-diagonaux et tableaux de Young},
	isbn = {978-3-540-47402-9},
	doi = {10.1007/BFb0072513},
	series = {Lecture Notes in Mathematics},
	abstract = {We consider path in the lattice of positive integer coordinate where the possible "moves" are of four kinds : (1) increasing the x coordinate by 1, (2) decreasing the x coordinate by 1, (3) increasing the y coordinate by 1, (4) decreasing the y coordinate by 1. The number of such paths of length ?, from (0,0) to any point whose y-coordinate is 0, lying below or touching the main diagonal, is {CnCn}+1 for ?=2n and Cn+1Cn+1 for ?=2n+1 where Cn is the Catalan number. We give a bijective proof of this result. As corollary we give exact formulas for the number of standard Young tableaux having n cells and a most k rows in the cases k=4 and k=5.},
	pages = {112--125},
	booktitle = {Combinatoire \'enum\'erative},
	publisher = {Springer},
	author = {Gouyou-Beauchamps, Dominique},
	editor = {Labelle, Gilbert and Leroux, Pierre},
	date = {1986},
	langid = {french},
	keywords = {Bijective Proof, Binomial Determinant, Catalan Number, Column Strict Tableau, Standard Young Tableau}
}

@article{hoggatt_palindromic_1975,
	title = {Palindromic compositions},
	volume = {13},
	issn = {0015-0517},
	url = {https://mathscinet.ams.org/mathscinet-getitem?mr=414477},
	pages = {350--356},
	number = {4},
	journaltitle = {Fibonacci Quart.},
	author = {Hoggatt, Jr., V. E. and Bicknell, Marjorie},
	date = {1975},
	mrnumber = {414477},
	file = {MathSciNet Snapshot:/Users/sergi/Zotero/storage/LM2UEL4P/publdoc.html:text/html}
}

@article{jungen_sur_1931,
	title = {Sur les s\'eries de Taylor n'ayant que des singularit\'es alg\'ebrico-logarithmiques sur leur cercle de convergence},
	volume = {3},
	issn = {0010-2571},
	doi = {10.1007/BF01601817},
	pages = {266--306},
	number = {1},
	journaltitle = {Comment. Math. Helv.},
	author = {Jungen, R.},
	date = {1931},
	mrnumber = {1509439},
	file = {MathSciNet Snapshot:/Users/sergi/Zotero/storage/DB7GITSY/publdoc.html:text/html;Submitted Version:/Users/sergi/Zotero/storage/KAETAZXC/Jungen - 1931 - Sur les s\'eries de Taylor n'ayant que des singulari.pdf:application/pdf}
}

@article{lipshitz_diagonal_1988,
	title = {The diagonal of a D-finite power series is D-finite},
	volume = {113},
	issn = {0021-8693},
	doi = {10.1016/0021-8693(88)90166-4},
	pages = {373--378},
	number = {2},
	journaltitle = {Journal of Algebra},
	author = {Lipshitz, Leonard},
	date = {1988-03-01},
	langid = {english},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/K3AGSYAK/Lipshitz - 1988 - The diagonal of a D-finite power series is D-finit.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/B474NW2B/0021869388901664.html:text/html}
}

@article{polya_number_1969,
	title = {On the number of certain lattice polygons},
	volume = {6},
	issn = {0021-9800},
	url = {https://mathscinet.ams.org/mathscinet-getitem?mr=236031},
	pages = {102--105},
	journaltitle = {J. Combinatorial Theory},
	author = {P\'olya, George},
	date = {1969},
	mrnumber = {236031},
	file = {MathSciNet Snapshot:/Users/sergi/Zotero/storage/7N2QIN5D/publdoc.html:text/html}
}

@article{prellberg_critical_1995,
	title = {Critical exponents from nonlinear functional equations for partially directed cluster models},
	volume = {78},
	issn = {1572-9613},
	doi = {10.1007/BF02183685},
	abstract = {We present a method for the derivation of the generating function and computation of critical exponents for several cluster models (staircase, bar-graph, and directed column-convex polygons, as well as partially directed self-avoiding walks), starting with nonlinear functional equations for the generating function. By linearizing these equations, we first give a derivation of the generating functions. The nonlinear equations are further used to compute the thermodynamic critical exponents via a formal perturbation ansatz. Alternatively, taking the continuum limit leads to nonlinear differential equations, from which one can extract the scaling function. We find that all the above models are in the same universality class with exponents ? u =-1/2, ? i =-1/3, and ?=2/3. All models have as their scaling function the logarithmic derivative of the Airy function.},
	pages = {701--730},
	number = {3},
	journaltitle = {J Stat Phys},
	author = {Prellberg, Thomas and Brak, Richard},
	date = {1995-02-01},
	langid = {english},
	keywords = {cluster models, critical exponents, Functional equations, nonlinear differential equation, polygons, scaling functions},
	file = {Springer Full Text PDF:/Users/sergi/Zotero/storage/KIIHS77R/Prellberg and Brak - 1995 - Critical exponents from nonlinear functional equat.pdf:application/pdf}
}

@article{shapiro_catalan_1976,
	title = {A Catalan triangle},
	volume = {14},
	issn = {0012-365X},
	doi = {10.1016/0012-365X(76)90009-1},
	abstract = {We develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted in terms of numbers of pairs of nonintersecting paths in the first quadrant. The main applications are results about the Catalan numbers and various random walk problems.},
	pages = {83--90},
	number = {1},
	journaltitle = {Discrete Mathematics},
	author = {Shapiro, Louis W.},
	date = {1976-01-01},
	langid = {english},
	file = {ScienceDirect Full Text PDF:/Users/sergi/Zotero/storage/M66357KT/Shapiro - 1976 - A Catalan triangle.pdf:application/pdf;ScienceDirect Snapshot:/Users/sergi/Zotero/storage/7EVUPH5U/0012365X76900091.html:text/html}
}

@article{elizalde_simple_2003,
	title = {A Simple and Unusual Bijection for Dyck Paths and its Consequences},
	volume = {7},
	issn = {0219-3094},
	doi = {10.1007/s00026-003-0186-y},
	abstract = {In this paper we introduce a new bijection from the set of Dyck paths to itself. This bijection has the property that it maps statistics that appeared recently in the study of patternavoiding permutations into classical statistics on Dyck paths, whose distribution is easy to obtain. We also present a generalization of the bijection, as well as several applications of it to enumeration problems of statistics in restricted permutations.},
	pages = {281--297},
	number = {3},
	journaltitle = {Ann. Combin.},
	author = {Elizalde, Sergi and Deutsch, Emeric},
	date = {2003-12-01},
	langid = {english},
	keywords = {bijections, Dyck paths, restricted permutations},
	file = {Springer Full Text PDF:/Users/sergi/Zotero/storage/FJG2JRIF/Elizalde and Deutsch - 2003 - A Simple and Unusual Bijection for Dyck Paths and .pdf:application/pdf}
}