20 citations · 184 across the 28 of their papers we have counts for
30 papers
An oral history of FPSAC
Sam Hopkins
As its 40th anniversary nears, we present a history of the International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), through interviews with figures from…
Invariance of rowmotion for variants of the Tamari lattice
Ben Adenbaum, Emily Barnard, Cesar Ceballos +6
We show that the rowmotion operator from dynamical algebraic combinatorics behaves the same on all alt -Tamari lattices for a fixed lattice path . We use this invariance of r…
RSK via local transformations
Sam Hopkins
We explain how to define the Robinson-Schensted-Knuth (RSK) correspondence in terms of local transformations called "toggles." (This note, which is not intended for publication and…
Combinatorial reciprocity for non-intersecting paths
Sam Hopkins, Gjergji Zaimi
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…
Restricted Birkhoff polytopes and Ehrhart period collapse
Per Alexandersson, Sam Hopkins, Gjergji Zaimi
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the "longest increasing subsequence" have Ehrhart quasi-polynomials w…
A note on Möbius functions of upho posets
Sam Hopkins
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 generatin…
On the -Enumeration of Barely Set-Valued Tableaux and Plane Partitions
Sam Hopkins, Alexander Lazar, Svante Linusson
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 enume…
Symmetry of Narayana numbers and rowvacuation of root posets
Colin Defant, Sam Hopkins
For a Weyl group of rank , the -Catalan number is the number of antichains of the poset of positive roots, and the -Narayana numbers refine the -Catalan number by k…
The birational Lalanne-Kreweras involution
Sam Hopkins, Michael Joseph
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…
Plane partitions of shifted double staircase shape
Sam Hopkins, Tri Lai
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 wit…
Order polynomial product formulas and poset dynamics
Sam Hopkins
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 behavio…
Promotion of Kreweras words
Sam Hopkins, Martin Rubey
Kreweras words are words consisting of n A's, n B's, and n C's in which every prefix has at least as many A's as B's and at least as many A's as C's. Equivalently, a Kreweras word…
Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotion
Sam Hopkins
We relate Reiner, Tenner, and Yong's coincidental down-degree expectations (CDE) property of posets to the minuscule doppelgänger pairs studied by Hamaker, Patrias, Pechenik, and W…
The CDE property for skew vexillary permutations
Sam Hopkins
We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree…
A positive formula for the Ehrhart-like polynomials from root system chip-firing
Sam Hopkins, Alexander Postnikov
In earlier work in collaboration with Pavel Galashin and Thomas McConville we introduced a version of chip-firing for root systems. Our investigation of root system chip-firing led…
Root system chip-firing I: Interval-firing
Pavel Galashin, Sam Hopkins, Thomas McConville +1
Jim Propp recently introduced a variant of chip-firing on a line where the chips are given distinct integer labels. Hopkins, McConville, and Propp showed that this process is confl…
Root system chip-firing II: Central-firing
Pavel Galashin, Sam Hopkins, Thomas McConville +1
Jim Propp recently proposed a labeled version of chip-firing on a line and conjectured that this process is confluent from some initial configurations. This was proved by Hopkins-M…
Sorting via chip-firing
Sam Hopkins, Thomas McConville, James Propp
We investigate a variant of the chip-firing process on the infinite path graph: rather than treating the chips as indistinguishable, we label them with positive integers. To fire a…
The CDE property for minuscule lattices
Sam Hopkins
Reiner, Tenner, and Yong recently introduced the coincidental down-degree expectations (CDE) property for finite posets and showed that many nice posets are CDE. In this paper we f…
Quantum integer-valued polynomials
Nate Harman, Sam Hopkins
We define a -deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkabl…
Fourientation activities and the Tutte polynomial
Spencer Backman, Sam Hopkins, Lorenzo Traldi
A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fo…
The expected jaggedness of order ideals
Melody Chan, Shahrzad Haddadan, Sam Hopkins +1
The jaggedness of an order ideal I in a poset P is the number of maximal elements in I plus the number of minimal elements of P not in I. A probability distribution on the set of o…
Parking functions and tree inversions revisited
Petar Gaydarov, Sam Hopkins
Kreweras proved that the reversed sum enumerator for parking functions of length is equal to the inversion enumerator for labeled trees on vertices. Recently, Perkinson,…
Fourientations and the Tutte Polynomial
Spencer Backman, Sam Hopkins
A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the…