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pro vyhledávání: '"Hopkins, Sam"'
Autor:
Hopkins, Sam
A poset is called upper homogeneous, or "upho," if every principal order filter of the poset is isomorphic to the whole poset. We study (finite type $\mathbb{N}$-graded) upho lattices, with an eye towards their classification. Any upho lattice has as
Externí odkaz:
http://arxiv.org/abs/2407.08013
Autor:
Hopkins, Sam, Zaimi, Gjergji
Publikováno v:
Enumerative Combinatorics and Applications, 3(2), 2023
We prove a combinatorial reciprocity theorem for the enumeration of non-intersecting paths in a linearly growing sequence of acyclic planar networks. We explain two applications of this theorem: reciprocity for fans of bounded Dyck paths, and recipro
Externí odkaz:
http://arxiv.org/abs/2301.00405
Publikováno v:
Discrete & Computational Geometry, 2024
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the "longest increasing subsequence" have Ehrhart quasi-polynomials which are honest polynomials, even though they are just rational polyto
Externí odkaz:
http://arxiv.org/abs/2206.02276
Autor:
Hopkins, Sam
Publikováno v:
Electronic Journal of Combinatorics, Volume 29, Issue 2 (2022), P2.39
A poset is called upper homogeneous (or "upho") if every principal order filter of the poset is isomorphic to the whole poset. We observe that the rank and characteristic generating functions of upho posets are multiplicative inverses of one another.
Externí odkaz:
http://arxiv.org/abs/2202.12103
Publikováno v:
Combinatorial Theory, 3(2), 2023
The rowmotion operator acting on the set of order ideals of a finite poset has been the focus of a significant amount of recent research. One of the major goals has been to exhibit homomesies: statistics that have the same average along every orbit o
Externí odkaz:
http://arxiv.org/abs/2108.13227
Publikováno v:
European Journal of Combinatorics, 113, 2023
Barely set-valued tableaux are a variant of Young tableaux in which one box contains two numbers as its entry. It has recently been discovered that there are product formulas enumerating certain classes of barely set-valued tableaux. We give some $q$
Externí odkaz:
http://arxiv.org/abs/2106.07418
Autor:
Defant, Colin, Hopkins, Sam
Publikováno v:
Forum of Mathematics, Sigma 9 (2021) e53
For a Weyl group $W$ of rank $r$, the $W$-Catalan number is the number of antichains of the poset of positive roots, and the $W$-Narayana numbers refine the $W$-Catalan number by keeping track of the cardinalities of these antichains. The $W$-Narayan
Externí odkaz:
http://arxiv.org/abs/2101.02329
Autor:
Hopkins, Sam, Joseph, Michael
Publikováno v:
Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 227-265
The Lalanne-Kreweras involution is an involution on the set of Dyck paths which combinatorially exhibits the symmetry of the number of valleys and major index statistics. We define piecewise-linear and birational extensions of the Lalanne-Kreweras in
Externí odkaz:
http://arxiv.org/abs/2012.15795
Autor:
Hopkins, Sam, Lai, Tri
Publikováno v:
Journal of Combinatorial Theory, Series A, 183, 2021
We give a product formula for the number of shifted plane partitions of shifted double staircase shape with bounded entries. This is the first new example of a family of shapes with a plane partition product formula in many years. The proof is based
Externí odkaz:
http://arxiv.org/abs/2007.05381
Autor:
Hopkins, Sam
Publikováno v:
In "Open Problems in Algebraic Combinatorics," Vol. 110 of Proceedings of Symposia in Pure Matehmatics, AMS, 2024
We survey all known examples of finite posets whose order polynomials have product formulas, and we propose the heuristic that these are the same posets with good dynamical behavior. Here the dynamics in question are the actions of promotion on the l
Externí odkaz:
http://arxiv.org/abs/2006.01568