@article{CdPBM04, title={Cayley lattices of finite Coxeter groups are bounded}, author={Caspard, Nathalie and de Poly-Barbut, Claude Le Conte and Morvan, Michel}, journal={Advances in Applied Mathematics}, volume={33}, number={1}, pages={71--94}, year={2004}, publisher={Elsevier} } @article {MD2020, AUTHOR = {M\'{e}sz\'{a}ros, Karola and St. Dizier, Avery}, TITLE = {From generalized permutahedra to {G}rothendieck polynomials via flow polytopes}, JOURNAL = {Algebr. Comb.}, FJOURNAL = {Algebraic Combinatorics}, VOLUME = {3}, YEAR = {2020}, NUMBER = {5}, PAGES = {1197--1229}, ISSN = {2589-5486}, } @article {LMMdiagonal2019, AUTHOR = {Liu, Ricky Ini and Morales, Alejandro H. and M\'{e}sz\'{a}ros, Karola}, TITLE = {Flow polytopes and the space of diagonal harmonics}, JOURNAL = {Canad. J. Math.}, FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de Math\'{e}matiques}, VOLUME = {71}, YEAR = {2019}, NUMBER = {6}, PAGES = {1495--1521}, ISSN = {0008-414X,1496-4279}, } @article{T23, title={Combinatorics of Permutreehedra and Geometry of $s$-Permutahedra}, author={Tamayo Jim{\'e}nez, Daniel}, eprint={2310.19732}, year={2023}, } @article {BGHHKMY19, AUTHOR = {Benedetti, Carolina and Gonz\'{a}lez D'Le\'{o}n, Rafael S. and Hanusa, Christopher R. H. and Harris, Pamela E. and Khare, Apoorva and Morales, Alejandro H. and Yip, Martha}, TITLE = {A combinatorial model for computing volumes of flow polytopes}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {372}, YEAR = {2019}, NUMBER = {5}, PAGES = {3369--3404}, MRCLASS = {05A15 (05A19 05C20 05C21 52A38 52B05 52B11)}, MRNUMBER = {3988614}, MRREVIEWER = {Ruriko Yoshida}, } @article{BGMY23, title={A Unifying Framework for the {$nu$}-Tamari Lattice and Principal Order Ideals in Young’s Lattice}, author={von Bell, Matias and Gonz{\'a}lez D’Le{\'o}n, Rafael S and Mayorga Cetina, Francisco A and Yip, Martha}, journal={Combinatorica}, pages={1--26}, year={2023}, publisher={Springer} } @article {BV08, AUTHOR = {Baldoni, Welleda and Vergne, Mich\`ele}, TITLE = {Kostant partitions functions and flow polytopes}, JOURNAL = {Transform. Groups}, FJOURNAL = {Transformation Groups}, VOLUME = {13}, YEAR = {2008}, NUMBER = {3-4}, PAGES = {447--469}, MRCLASS = {52B12 (05A17 11D45 52C35)}, MRNUMBER = {2452600}, MRREVIEWER = {Jes\'{u}s A. De Loera}, } @misc{CC23, AUTHOR = {Ceballos, Cesar and Chenevi{\`e}re, Cl{\'e}ment}, EPRINT = {2305.02250}, EPRINTTYPE = {arxiv}, TITLE = {On linear intervals in the alt {$\nu$}-Tamari lattices}, YEAR = {2023}} @article{CP22, title={The $s$-weak order and $s$-permutahedra I: combinatorics and lattice structure}, author={Ceballos, Cesar and Pons, Viviane}, journal={arXiv preprint arXiv:2212.11556}, year={2022} } @article{Day77, title={Splitting lattices generate all lattices}, author={Day, Alan}, journal={Algebra Universalis}, volume={7}, pages={163--169}, year={1977}, publisher={Springer} } @incollection {DKK12, AUTHOR = {Danilov, Vladimir I. and Karzanov, Alexander V. and Koshevoy, Gleb A.}, TITLE = {Coherent fans in the space of flows in framed graphs}, BOOKTITLE = {24th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2012)}, SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AR}, PAGES = {481--490}, YEAR = {2012}, MRCLASS = {05C21 (05E18)}, MRNUMBER = {2958022}, } @article{GMPTY23, title={Realizing the $ s $-permutahedron via flow polytopes}, author={Gonz{\'a}lez D'Le{\'o}n, Rafael S. and Morales, Alejandro H. and Philippe, Eva and Tamayo Jim{\'e}nez, Daniel and Yip, Martha}, eprint={2307.03474}, year={2023} } @article{GV85, title={Binomial determinants, paths, and hook length formulae}, author={Gessel, Ira and Viennot, G{\'e}rard}, journal={Advances in mathematics}, volume={58}, number={3}, pages={300--321}, year={1985}, publisher={Elsevier} } @book{GW16, title={Lattice theory: special topics and applications}, author={Gratzer, George A and Wehrung, Friedrich}, year={2016}, publisher={Springer} } @article {MM19, AUTHOR = {M\'{e}sz\'{a}ros, Karola and Morales, Alejandro H.}, TITLE = {Volumes and {E}hrhart polynomials of flow polytopes}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {293}, YEAR = {2019}, NUMBER = {3-4}, PAGES = {1369--1401}, MRCLASS = {52B20 (05C90)}, MRNUMBER = {4024590}, MRREVIEWER = {Matthias Beck}, } @article {MMS19, AUTHOR = {M\'{e}sz\'{a}ros, Karola and Morales, Alejandro H. and Striker, Jessica}, TITLE = {On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {62}, YEAR = {2019}, NUMBER = {1}, PAGES = {128--163}, MRCLASS = {52B12 (05A05 05A19 05A20 05C10 05C21 52B05 52B22)}, MRNUMBER = {3959924}, MRREVIEWER = {Robert Davis}, } @article{Pil20, title={Cambrian triangulations and their tropical realizations}, author={Pilaud, Vincent}, journal={European Journal of Combinatorics}, volume={83}, pages={102997}, year={2020}, publisher={Elsevier} } @article {PS02, AUTHOR = {Pitman, Jim and Stanley, Richard P.}, TITLE = {A polytope related to empirical distributions, plane trees, parking functions, and the associahedron}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {27}, YEAR = {2002}, NUMBER = {4}, PAGES = {603--634}, MRCLASS = {52B11 (05A15 60C05)}, MRNUMBER = {1902680}, MRREVIEWER = {Igor Rivin}, } @article {PV17, AUTHOR = {Pr\'{e}ville-Ratelle, Louis-Fran\c{c}ois and Viennot, Xavier}, TITLE = {The enumeration of generalized {T}amari intervals}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {369}, YEAR = {2017}, NUMBER = {7}, PAGES = {5219--5239}, MRCLASS = {05A15 (05C30 05E10 05E40 06A07)}, MRNUMBER = {3632566}, MRREVIEWER = {Konrad P. Pi\'{o}ro}, } @article{Rea06, title={Cambrian lattices}, author={Reading, Nathan}, journal={Advances in Mathematics}, volume={205}, number={2}, pages={313--353}, year={2006}, publisher={Elsevier} } @article{Sta80, title={Decompositions of rational convex polytopes}, author={Stanley, Richard P.}, journal={Ann. Discrete Math}, volume={6}, number={6}, pages={333--342}, year={1980} } @article {Sta86, AUTHOR = {Stanley, Richard P.}, TITLE = {Two poset polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {1}, YEAR = {1986}, NUMBER = {1}, PAGES = {9--23}, MRCLASS = {52A25 (52A40)}, MRNUMBER = {824105}, MRREVIEWER = {P. McMullen}, } @book{Ziegler07, AUTHOR = {Ziegler, G{\"u}nter M}, TITLE = {Lectures on polytopes}, VOLUME = {152}, YEAR = {2007}, PUBLISHER = {Springer Science \& Business Media} }