%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for Nick Beaton at 2019-05-25 21:37:02 +1000 


%% Saved with string encoding Unicode (UTF-8) 



@article{FZ07,
	Author = {Fomin, S. and Zelevinsky, A.},
	Fjournal = {Compositio Mathematica},
	Journal = {Compos. Math.},
	Mrclass = {16S99 (05E15 14M17 22E46)},
	Mrnumber = {2295199},
	Mrreviewer = {Christof Gei\ss},
	Number = {1},
	Pages = {112--164},
	Title = {Cluster algebras. {IV}. {C}oefficients},
	Volume = {143},
	Year = {2007}}

@article{BFZ05,
	Author = {Berenstein, A. and Fomin, S. and Zelevinsky, A.},
	Date-Modified = {2019-05-25 21:28:41 +1000},
	Doi = {10.1215/s0012-7094-04-12611-9},
	Fjournal = {Duke Mathematical Journal},
	Journal = {Duke Math. J.},
	Mrclass = {16S99 (05E15 14M17 22E46)},
	Mrnumber = {2110627},
	Number = {1},
	Pages = {1--52},
	Title = {Cluster algebras. {III}. {U}pper bounds and double {B}ruhat cells},
	Volume = {126},
	Year = {2005}}

@article{BM09,
	Author = {Baur, K. and Marsh, R. J.},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E15 (13F60)},
	Mrnumber = {2545501},
	Number = {3},
	Pages = {349--379},
	Title = {Frieze patterns for punctured discs},
	Volume = {30},
	Year = {2009}}

@article{BMRRT06,
	Author = {Buan, A. and Marsh, R. and Reineke, M. and Reiten, I. and Todorov, G.},
	Date-Modified = {2019-05-25 21:29:18 +1000},
	Doi = {10.1016/j.aim.2005.06.003},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Mrclass = {16G20 (16G70 16S99)},
	Mrnumber = {2249625},
	Mrreviewer = {Lidia Angeleri H\"{u}gel},
	Number = {2},
	Pages = {572--618},
	Title = {Tilting theory and cluster combinatorics},
	Volume = {204},
	Year = {2006}}

@article{BFGST18,
	Author = {Baur, K. and Faber, E. and Gratz, S. and Serhiyenko, Khrystyna and Todorov, Gordana},
	Fjournal = {Bulletin des Sciences Math\'ematiques},
	Journal = {Bull. Sci. Math.},
	Mrclass = {16G20 (05E15 18D99)},
	Mrnumber = {3758161},
	Pages = {1--48},
	Title = {Mutation of friezes},
	Volume = {142},
	Year = {2018}}

@article{FZ03,
	Author = {Fomin, S. and Zelevinsky, A.},
	Fjournal = {Inventiones Mathematicae},
	Journal = {Invent. Math.},
	Mrclass = {17B20 (05E15 16S99 52B12)},
	Mrnumber = {2004457},
	Mrreviewer = {Eric N. Sommers},
	Number = {1},
	Pages = {63--121},
	Title = {Cluster algebras. {II}. {F}inite type classification},
	Volume = {154},
	Year = {2003}}

@article{ARS10,
	Author = {Assem, Ibrahim and Reutenauer, Christophe and Smith, David},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Mrclass = {13F60 (05A15 05C50 05C75 17B22)},
	Mrnumber = {2729004},
	Mrreviewer = {Kyungyong Lee},
	Number = {6},
	Pages = {3134--3165},
	Title = {Friezes},
	Volume = {225},
	Year = {2010}}

@article{BPT16,
	Author = {Baur, K. and Parsons, M. J. and Tschabold, M.},
	Fjournal = {European Journal of Combinatorics},
	Journal = {European J. Combin.},
	Mrclass = {05E15},
	Mrnumber = {3459066},
	Mrreviewer = {Kyungyong Lee},
	Pages = {220--237},
	Title = {Infinite friezes},
	Volume = {54},
	Year = {2016}}

@article{CCS06,
	Author = {Caldero, P. and Chapoton, F. and Schiffler, R.},
	Date-Modified = {2019-05-25 21:30:38 +1000},
	Doi = {10.1090/s0002-9947-05-03753-0},
	Fjournal = {Transactions of the American Mathematical Society},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {16G20 (05E15 16G70)},
	Mrnumber = {2187656},
	Mrreviewer = {Dirk Kussin},
	Number = {3},
	Pages = {1347--1364},
	Title = {Quivers with relations arising from clusters ({$A_n$} case)},
	Volume = {358},
	Year = {2006}}

@article{ConCox73,
	Author = {Conway, J. H. and Coxeter, H. S. M.},
	Date-Modified = {2019-05-25 21:31:39 +1000},
	Doi = {10.2307/3615344},
	Fjournal = {The Mathematical Gazette},
	Journal = {Math. Gaz.},
	Mrclass = {50B30},
	Mrnumber = {0461269, 0461270},
	Pages = {87--94, 175--183},
	Title = {Triangulated polygons and frieze patterns},
	Volume = {57},
	Year = {1973}}

@article{Cox71,
	Author = {Coxeter, H. S. M.},
	Fjournal = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
	Journal = {Acta Arith.},
	Mrclass = {10.55 (01.00)},
	Mrnumber = {0286771},
	Mrreviewer = {D. A. Klarner},
	Pages = {297--310},
	Title = {Frieze patterns},
	Volume = {18},
	Year = {1971}}

@article{FP16,
	Author = {Fontaine, B. and Plamondon, P.-G.},
	Date-Modified = {2019-05-25 21:34:25 +1000},
	Doi = {10.1007/s10801-016-0675-9},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E15 (13F60)},
	Mrnumber = {3533561},
	Number = {2},
	Pages = {433--445},
	Title = {Counting friezes in type {$D_n$}},
	Volume = {44},
	Year = {2016}}

@misc{Fon14,
	Author = {Fontaine, B.},
	Eprint = {1409.6026},
	Eprinttype = {arxiv},
	Title = {Non-zero integral friezes},
	Year = {2014}}

@article{FST08,
	Author = {Fomin, S. and Shapiro, M. and Thurston, D.},
	Date-Modified = {2019-05-25 21:33:24 +1000},
	Doi = {10.1007/s11511-008-0030-7},
	Fjournal = {Acta Mathematica},
	Journal = {Acta Math.},
	Mrclass = {57Q15 (13F60 32G15 52B70)},
	Mrnumber = {2448067},
	Mrreviewer = {Christof Gei\ss},
	Number = {1},
	Pages = {83--146},
	Title = {Cluster algebras and triangulated surfaces. {I}. {C}luster complexes},
	Volume = {201},
	Year = {2008}}

@misc{GS18,
	Author = {Gunawan, E. and Schiffler, R.},
	Eprint = {1806.00940},
	Eprinttype = {arxiv},
	Title = {Frieze Vectors and Unitary Friezes},
	Year = {2018}}

@article{KS11,
	Author = {Keller, B. and Scherotzke, S.},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Mrclass = {13F60 (16G20)},
	Mrnumber = {2824571},
	Mrreviewer = {Xueqing Chen},
	Number = {3},
	Pages = {1842--1862},
	Title = {Linear recurrence relations for cluster variables of affine quivers},
	Volume = {228},
	Year = {2011}}

@article{LS15,
	Author = {Lee, K. and Schiffler, R.},
	Date-Modified = {2019-05-25 21:35:06 +1000},
	Doi = {10.4007/annals.2015.182.1.2},
	Fjournal = {Annals of Mathematics. Second Series},
	Journal = {Ann. of Math. (2)},
	Mrclass = {13F60 (05E15)},
	Mrnumber = {3374957},
	Mrreviewer = {Alfredo N\'{a}jera Ch\'{a}vez},
	Number = {1},
	Pages = {73--125},
	Title = {Positivity for cluster algebras},
	Volume = {182},
	Year = {2015}}

@online{oeisD,
	Url = {oeis.org/A247415},
	Bdsk-Url-1 = {oeis.org/A247415}}

@online{oeisB,
	Url = {oeis.org/A247416},
	Bdsk-Url-1 = {oeis.org/A247416}}

@article{Mor12,
	Author = {Morier-Genoud, S.},
	Date-Modified = {2019-05-25 21:35:40 +1000},
	Doi = {10.1007/s10801-012-0348-2},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E15 (13F60)},
	Mrnumber = {2984155},
	Mrreviewer = {Kyungyong Lee},
	Number = {4},
	Pages = {515--539},
	Title = {Arithmetics of 2-friezes},
	Volume = {36},
	Year = {2012}}

@article{Mor15,
	Author = {Morier-Genoud, S.},
	Date-Modified = {2019-05-25 21:36:18 +1000},
	Doi = {10.1112/blms/bdv070},
	Fjournal = {Bulletin of the London Mathematical Society},
	Journal = {Bull. Lond. Math. Soc.},
	Mrclass = {05E10 (13F60 14M15 16G20 39A70)},
	Mrnumber = {3431573},
	Mrreviewer = {Kyungyong Lee},
	Number = {6},
	Pages = {895--938},
	Title = {Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics},
	Volume = {47},
	Year = {2015}}

@article{MOT15,
	Author = {Morier-Genoud, S. and Ovsienko, V. and Tabachnikov, S.},
	Fjournal = {L'Enseignement Math\'ematique},
	Journal = {Enseign. Math.},
	Mrclass = {05E10 (05A15 11B57)},
	Mrnumber = {3449283},
	Mrreviewer = {Seyed Amin Seyed Fakhari},
	Number = {1-2},
	Pages = {71--92},
	Title = {{${\rm SL}_2(\Bbb{Z})$}-tilings of the torus, {C}oxeter-{C}onway friezes and {F}arey triangulations},
	Volume = {61},
	Year = {2015}}

@article{MW13,
	Author = {Musiker, G. and Williams, L.},
	Fjournal = {International Mathematics Research Notices. IMRN},
	Journal = {Int. Math. Res. Not. IMRN},
	Mrclass = {13F60},
	Mrnumber = {3072996},
	Mrreviewer = {Yu Zhou},
	Number = {13},
	Pages = {2891--2944},
	Title = {Matrix formulae and skein relations for cluster algebras from surfaces},
	Year = {2013}}

@article{MSW11,
	Author = {Musiker, G. and Schiffler, R. and Williams, L.},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Mrclass = {13F60 (05C70 05E15)},
	Mrnumber = {2807089},
	Mrreviewer = {Gregoire Dupont},
	Number = {6},
	Pages = {2241--2308},
	Title = {Positivity for cluster algebras from surfaces},
	Volume = {227},
	Year = {2011}}

@article{Sch08,
	Author = {Schiffler, R.},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Journal = {J. Algebraic Combin.},
	Mrclass = {16G10 (05A15 16D90 18E30)},
	Mrnumber = {2366159},
	Mrreviewer = {Xiuping Su},
	Number = {1},
	Pages = {1--21},
	Title = {A geometric model for cluster categories of type {$D_n$}},
	Volume = {27},
	Year = {2008}}

@book{Schiffler,
	Author = {Schiffler, R.},
	Date-Modified = {2019-05-25 21:37:01 +1000},
	Mrclass = {16G20 (16G70)},
	Mrnumber = {3308668},
	Mrreviewer = {Alex Martsinkovsky},
	Publisher = {Springer, Cham},
	Series = {CMS Books in Mathematics/Ouvrages de Math\'{e}matiques de la SMC},
	Title = {Quiver Representations},
	Year = {2014}}

@article{BCI74,
	Author = {Broline, D. and Crowe, D. W. and Isaacs, I. M.},
	Fjournal = {Geometriae Dedicata},
	Journal = {Geometriae Dedicata},
	Mrclass = {05B30 (52A45)},
	Mrnumber = {0363955},
	Mrreviewer = {G. L. Alexanderson},
	Pages = {171--176},
	Title = {The geometry of frieze patterns},
	Volume = {3},
	Year = {1974}}

@article{CC06,
	Author = {Caldero, P. and Chapoton, F.},
	Date-Modified = {2019-05-25 21:29:54 +1000},
	Doi = {10.4171/cmh/65},
	Fjournal = {Commentarii Mathematici Helvetici. A Journal of the Swiss Mathematical Society},
	Journal = {Comment. Math. Helv.},
	Mrclass = {16G20 (18E30)},
	Mrnumber = {2250855},
	Number = {3},
	Pages = {595--616},
	Title = {Cluster algebras as {H}all algebras of quiver representations},
	Volume = {81},
	Year = {2006}}

@article{CS18,
	Author = {\c{C}anak\c{c}\i , \.{I}. and Schiffler, R.},
	Fjournal = {Compositio Mathematica},
	Journal = {Compos. Math.},
	Mrclass = {13F60 (11A55 30B70)},
	Mrnumber = {3778183},
	Number = {3},
	Pages = {565--593},
	Title = {Cluster algebras and continued fractions},
	Volume = {154},
	Year = {2018}}

@article{CS13,
	Author = {\c{C}anak\c{c}\i , \.{I}. and Schiffler, R.},
	Fjournal = {Journal of Algebra},
	Journal = {J. Algebra},
	Mrclass = {13F60 (05Exx)},
	Mrnumber = {3034481},
	Mrreviewer = {Xueqing Chen},
	Pages = {240--281},
	Title = {Snake graph calculus and cluster algebras from surfaces},
	Volume = {382},
	Year = {2013}}

@article{FZ02,
	Author = {Fomin, S. and Zelevinsky, A.},
	Date-Modified = {2019-05-25 21:33:53 +1000},
	Doi = {10.1090/s0894-0347-01-00385-x},
	Fjournal = {Journal of the American Mathematical Society},
	Journal = {J. Amer. Math. Soc.},
	Mrclass = {16S99 (14M99 17B99)},
	Mrnumber = {1887642},
	Mrreviewer = {Eric N. Sommers},
	Number = {2},
	Pages = {497--529},
	Title = {Cluster algebras. {I}. {F}oundations},
	Volume = {15},
	Year = {2002}}

@article{GM15,
	Author = {Gunawan, E. and Musiker, G.},
	Fjournal = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications},
	Journal = {SIGMA Symmetry Integrability Geom. Methods Appl.},
	Mrclass = {13F60 (05E15 16S99)},
	Mrnumber = {3373632},
	Pages = {060, 46 pages},
	Title = {{$T$}-path formula and atomic bases for cluster algebras of type {$D$}},
	Volume = {11},
	Year = {2015}}

@article{LLN17,
	Author = {Lee, K. and Li, L. and Nguyen, B.},
	Fjournal = {Electronic Journal of Combinatorics},
	Journal = {Electron. J. Combin.},
	Mrclass = {13F60 (05A19 05E40)},
	Mrnumber = {3665575},
	Mrreviewer = {Ralf Schiffler},
	Number = {2},
	Pages = {Paper 2.42, 41},
	Title = {New combinatorial formulas for cluster monomials of type {$A$} quivers},
	Volume = {24},
	Year = {2017}}

@article{LRS17,
	Author = {Leroy, J. and Rigo, M. and Stipulanti, M.},
	Fjournal = {Discrete Mathematics},
	Journal = {Discrete Math.},
	Mrclass = {05A15 (05A05 11B65 68R15)},
	Mrnumber = {3612418},
	Mrreviewer = {Zhiyong Zhu},
	Number = {5},
	Pages = {862--881},
	Title = {Counting the number of non-zero coefficients in rows of generalized {P}ascal triangles},
	Volume = {340},
	Year = {2017}}

@article{MSW11,
	Author = {Musiker, G. and Schiffler, R. and Williams, L.},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Mrclass = {13F60 (05C70 05E15)},
	Mrnumber = {2807089},
	Mrreviewer = {Gregoire Dupont},
	Number = {6},
	Pages = {2241--2308},
	Title = {Positivity for cluster algebras from surfaces},
	Volume = {227},
	Year = {2011}}

@article{MSW13,
	Author = {Musiker, G. and Schiffler, R. and Williams, L.},
	Fjournal = {Compositio Mathematica},
	Journal = {Compos. Math.},
	Mrclass = {13F60 (05C70 05E15)},
	Mrnumber = {3020308},
	Mrreviewer = {Olga Kravchenko},
	Number = {2},
	Pages = {217--263},
	Title = {Bases for cluster algebras from surfaces},
	Volume = {149},
	Year = {2013}}

@article{ST09,
	Author = {Schiffler, R. and Thomas, H.},
	Fjournal = {International Mathematics Research Notices. IMRN},
	Journal = {Int. Math. Res. Not.},
	Number = {17},
	Pages = {3160--3189},
	Title = {On cluster algebras arising from unpunctured surfaces},
	Volume = {2009},
	Year = {2009}}