@misc{GYP, title={Hook formulas for linear extensions of mobile posets}, author = {Park, G.Y.}, note={in preparation}, year={2020} } @misc{OEIS, title={The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences}, author={N. J. A. Sloane}, note={published electronically at \url{https://oeis.org}} } @article{St71p2, title={Theory and application of plane partitions. Part 2}, author={Stanley, R. P.}, journal={Stud. Appl. Math.}, volume={50}, number={3}, pages={259--279}, year={1971}, publisher={Wiley Online Library} } @article {Thrall, AUTHOR = {Thrall, R. M.}, TITLE = {A combinatorial problem}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {Michigan Mathematical Journal}, VOLUME = {1}, YEAR = {1952}, PAGES = {81--88}, ISSN = {0026-2285}, MRCLASS = {09.0X}, MRREVIEWER = {J. Riguet}, URL = {http://projecteuclid.org/euclid.mmj/1028989731} } @article{JMcC, author={Jiradilok, P. and McConville, T.}, title = {Roots of descent polynomials and an algebraic inequality on hook lengths}, archivePrefix = "arXiv", eprintype = "arXiv", eprint = {1910.14631}, year = 2019 } @article {Stanqdes, AUTHOR = {Stanley, R. P.}, TITLE = {Binomial posets, {M}\"{o}bius inversion, and permutation enumeration}, JOURNAL = {J. Combinatorial Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {20}, YEAR = {1976}, NUMBER = {3}, PAGES = {336--356}, ISSN = {0097-3165}, MRCLASS = {05A15}, MRREVIEWER = {L. Carlitz}, DOI = {10.1016/0097-3165(76)90028-5}, URL = {https://doi-org.libproxy.uoregon.edu/10.1016/0097-3165(76)90028-5}, } @article {ProHLF, author = {Proctor, R. A.}, title = {$d$-complete posets generalize {Y}oung diagrams for the hook product formula: Partial Presentation of Proof}, journal = {RIMS K\^{o}ky\^{u}roku}, pages = {120--140}, year = {2014}, volume = {1913} } @article {Okada, AUTHOR = {Okada, S.}, TITLE = {{$(q,t)$}-deformations of multivariate hook product formulae}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {32}, YEAR = {2010}, NUMBER = {3}, PAGES = {399--416}, ISSN = {0925-9899}, MRCLASS = {05A17 (05A15 05E05 06A07)}, MRREVIEWER = {T. Kyle Petersen}, DOI = {10.1007/s10801-010-0221-0}, URL = {https://doi.org/10.1007/s10801-010-0221-0}, } @Article{Proctor2018, author="Proctor, R. A. and Scoppetta, L. M.", title="d-Complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions", journal="Order", year="2018", month="Oct", day="26", abstract="Although d-complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on their local structure. These posets are a mutual generalization of rooted trees, shapes, and shifted shapes. They possess Stanley's hook product property for their P-partition generating functions and Sch{\"u}tzenberger's well-defined jeu de taquin rectification property. The original definition of d-complete poset was lengthy, but more succinct definitions were later developed. Here several definitions are shown to be equivalent. The basic properties of d-complete posets are summarized. Background and a partial bibliography for these posets is given.", issn="1572-9273", doi="10.1007/s11083-018-9473-4", url="https://doi.org/10.1007/s11083-018-9473-4" } @article {ProctorScoppetta, AUTHOR = {Proctor, R. A. and Scoppetta, L. M.}, TITLE = {{$d$}-complete posets: local structural axioms, properties, and equivalent definitions}, JOURNAL = {Order}, VOLUME = {36}, YEAR = {2019}, NUMBER = {3}, PAGES = {399--422}, ISSN = {0167-8094}, MRCLASS = {06A07}, MRREVIEWER = {Frank Sottile}, DOI = {10.1007/s11083-018-9473-4}, URL = {https://doi.org/10.1007/s11083-018-9473-4}, } @article {ProClass, AUTHOR = {Proctor, R. A.}, TITLE = {Dynkin diagram classification of {$\lambda$}-minuscule {B}ruhat lattices and of {$d$}-complete posets}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {9}, YEAR = {1999}, NUMBER = {1}, PAGES = {61--94}, ISSN = {0925-9899}, MRCLASS = {06A07 (05E25)}, MRREVIEWER = {Gerhard Behrendt}, DOI = {10.1023/A:1018615115006}, } @article{NO, author = {Naruse, H. and Okada, S.}, title = {Skew hook formula for $d$-complete posets via equivariant $K$-theory}, journal = {Algebraic Combinatorics}, publisher = {MathOA foundation}, volume = {2}, number = {4}, year = {2019}, pages = {541-571}, doi = {10.5802/alco.54}, language = {en}, url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_4_541_0} } @article {MPP1, AUTHOR = {Morales, A. H. and Pak, I. and Panova, G.}, TITLE = {Hook formulas for skew shapes {I}. {$q$}-analogues and bijections}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {154}, YEAR = {2018}, PAGES = {350--405}, ISSN = {0097-3165}, MRCLASS = {05A19 (05A05 05A17 05E05)}, MRREVIEWER = {Sergi Elizalde}, DOI = {10.1016/j.jcta.2017.09.002}, URL = {https://doi.org/10.1016/j.jcta.2017.09.002}, } @article {MPP2, AUTHOR = {Morales, A. H. and Pak, I. and Panova, G.}, TITLE = {Hook formulas for skew shapes {II}. {C}ombinatorial proofs and enumerative applications}, JOURNAL = {SIAM J. Discrete Math.}, FJOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {31}, YEAR = {2017}, NUMBER = {3}, PAGES = {1953--1989}, ISSN = {0895-4801}, MRCLASS = {05A19 (05A05 05A15 05E05)}, MRREVIEWER = {Sergi Elizalde}, DOI = {10.1137/16M1099625}, URL = {https://doi.org/10.1137/16M1099625}, } @mastersthesis{grosser, title={Determinant Formulas for Counting Linear Extensions of Tree Posets}, type = "Undergraduate Honors Thesis", school={UMass, Amherst, Commonwealth Honors College}, note={available at \url{https://people.math.umass.edu/~ahmorales/mentoring/thesis_Grosser.pdf}}, author={Grosser, S.}, year={2018} } @article {BBS, AUTHOR = {Billey, S. and Burdzy, K. and Sagan, B. E.}, TITLE = {Permutations with given peak set}, JOURNAL = {J. Integer Seq.}, FJOURNAL = {Journal of Integer Sequences}, VOLUME = {16}, YEAR = {2013}, NUMBER = {6}, PAGES = {Article 13.6.1, 18}, ISSN = {1530-7638}, MRCLASS = {05A05 (05A10 05A15)}, MRREVIEWER = {Svetlana Poznanovi\'{c}}, } @article {foulkes, AUTHOR = {Foulkes, H. O.}, TITLE = {Enumeration of permutations with prescribed up-down and inversion sequences}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {15}, YEAR = {1976}, NUMBER = {3}, PAGES = {235--252}, ISSN = {0012-365X}, MRCLASS = {05A15 (20C30)}, MRREVIEWER = {Cheryl E. Praeger}, DOI = {10.1016/0012-365X(76)90028-5}, URL = {https://doi.org/10.1016/0012-365X(76)90028-5}, } @article{garvermatherne, author = {Garver, A. and Igusa, K. and Matherne, J. and Ostroff, J.}, title = {Combinatorics of exceptional sequences in type {A}}, journal = {Electron. J. Combin.}, year = 2019, pages= {1-20}, volume=26 } @article{aitken1943xxvi, title={The Monomial Expansion of Determinantal Symmetric Functions}, author={Aitken, A. C.}, journal={Proceedings of the Royal Society of Edinburgh Section A: Mathematics}, volume={61}, number={3}, pages={300--310}, year={1943}, publisher={Royal Society of Edinburgh Scotland Foundation} } @book{CA, place={Chelsea, NY}, title = {Combinatory Analysis {V}ol. {I}, {II} (bound in one volume)}, author = {MacMahon, P. A.}, publisher = {Dover Phoenix Editions. Dover Publications, Inc., Mineola, NY, 2004. Reprint of {\i}t An introduction to combinatory analysis (1920) and {\i}t Combinatory analysis. Vol. I, II}, year={1915, 1916} } @article{diaz2019descent, title={Descent polynomials}, author={Diaz-Lopez, A. and Harris, P. E. and Insko, E. and Omar, M. and Sagan, B. 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Series A}, VOLUME = {162}, YEAR = {2019}, PAGES = {167--221}, ISSN = {0097-3165}, MRCLASS = {06A07 (05A15 05A30)}, DOI = {10.1016/j.jcta.2018.11.003}, URL = {https://doi.org/10.1016/j.jcta.2018.11.003}, } @article{atk, title={On Computing the Number of Linear Extensions of a Tree}, volume={7}, journal={Order}, author={Atkinson, M. D.}, year={1990}, pages={23--25}} @article{q_hook, title={q-Hook length formulas for forests}, volume={52}, DOI={10.1016/0097-3165(89)90028-9}, number={2}, journal={Journal of Combinatorial Theory, Series A}, author={Bj\"{o}rner, A. and Wachs, M. L.}, year={1989}, pages={165--187}} @article {reglab, AUTHOR = {Bj\"{o}rner, A. and Wachs, M. L.}, TITLE = {Permutation statistics and linear extensions of posets}, JOURNAL = {Journal of Combinatorial Theory, Series A}, VOLUME = {58}, YEAR = {1991}, NUMBER = {1}, PAGES = {85--114}, ISSN = {0097-3165}, MRCLASS = {06A07 (05E99 20B35)}, MRREVIEWER = {Sergey V. Fomin}, DOI = {10.1016/0097-3165(91)90075-R}, URL = {https://doi.org/10.1016/0097-3165(91)90075-R}, } @article{alt, title= {Type $\mathbb{A}_n$ Exceptional Sequences }, author={Garver, A. and Matherne, J.}} @article {bw91, AUTHOR = {Brightwell, G. and Winkler, P.}, TITLE = {Counting linear extensions}, JOURNAL = {Order}, FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its Applications}, VOLUME = {8}, YEAR = {1991}, NUMBER = {3}, PAGES = {225--242}, ISSN = {0167-8094}, MRCLASS = {06A06 (68Q25)}, MRREVIEWER = {Christoph Meinel}, DOI = {10.1007/BF00383444}, } @article {dwyerelizalde, AUTHOR = {Dwyer, T. and Elizalde, S.}, TITLE = {Wilf equivalence relations for consecutive patterns}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {99}, YEAR = {2018}, PAGES = {134--157}, ISSN = {0196-8858}, MRCLASS = {05A05 (05A15 06A07)}, MRREVIEWER = {Nik Lygeros}, DOI = {10.1016/j.aam.2018.04.007}, URL = {https://doi.org/10.1016/j.aam.2018.04.007}, } @ARTICLE{dp18, author = {{Dittmer}, S. and {Pak}, I.}, title = "{Counting linear extensions of restricted posets}", archivePrefix = "arXiv", eprinttype = "arXiv", eprint = {1802.06312}, primaryClass = "math.CO", keywords = {Mathematics - Combinatorics}, year = 2018, adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180206312D}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article {p99, AUTHOR = {Proctor, R. A.}, TITLE = {Minuscule elements of {W}eyl groups, the numbers game, and {$d$}-complete posets}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {213}, YEAR = {1999}, NUMBER = {1}, PAGES = {272--303}, ISSN = {0021-8693}, MRCLASS = {05E15 (17B67)}, MRREVIEWER = {Godofredo Iommi Amun\'{a}tegui}, DOI = {10.1006/jabr.1998.7648}, } @article{frame1954hook, title={The hook graphs of the symmetric group}, author={Frame, J. S. and Robinson, G. de B. and Thrall, R. M.}, journal={Canadian Journal of Mathematics}, volume={6}, pages={316--324}, year={1954}, publisher={Cambridge University Press} } @incollection{mohring1989computationally, title={Computationally tractable classes of ordered sets}, author={M{\"o}hring, R. H.}, booktitle={Algorithms and order}, pages={105--193}, year={1989}, publisher={Springer} } @article{garver2020counting, title={Counting linear extensions of posets with determinants of hook lengths}, author={Garver, A. and Grosser, S. and Matherne, J. P. and Morales, A. H.}, journal = {SIAM Journal on Discrete Mathematics}, volume = {35}, number = {1}, pages = {205-233}, year = {2021}, doi = {10.1137/20M1320730} } @article{gessel1993counting, title={Counting permutations with given cycle structure and descent set}, author={Gessel, I. M. and Reutenauer, C.}, journal={Journal of Combinatorial Theory, Series A}, volume={64}, number={2}, pages={189--215}, year={1993}, publisher={Elsevier} }