AlCoVE 2024 will be held virtually on Zoom on June 17 – 18, 2024 (Monday and Tuesday).
Past conferences: AlCoVE 2020, AlCoVE 2021, AlCoVE 2022, and AlCoVE 2023.
Organizers: Laura Colmenarejo, Maria Gillespie, Oliver Pechenik, and Liam Solus
Conference poster: Download here.
AlCoVE brings together researchers interested in algebraic combinatorics from around the world. Each talk will be 30 minutes and between talks, there will be casual social activities for spending time with your friends and making new friends.
Registration and poster session application
To access the Zoom links, you must first register for the conference:
We will be holding virtual poster sessions in Gather on June 17 and June 18. Please submit a short application to present a poster HERE by the end of the day Eastern time on April 15.
List of Confirmed Speakers:
- José Aliste-Prieto, Universidad Andrés Bello
- Matthias Beck, San Francisco State University
- Sarah Brauner, LaCIM
- Christian Gaetz, Cornell University
- Sam Hopkins, Howard University
- Ezgi Kantarcı Oğuz, Galatasaray University
- Eric Marberg, HKUST
- Greta Panova, University of Southern California
- Anna Pun, CUNY-Baruch College
- Dominic Searles, University of Otago
- Kris Shaw, University of Oslo
- Vasu Tewari, University of Toronto Mississauga
Schedule (subject to change, all times EDT):
TBA. The password for Zoom and Gather is the same, and will be sent to registered participants.
JUNE 17 (MONDAY):
| 10:00 - 10:30 AM | Welcome | Zoom link | |||
| 10:30 - 11:00 | Matthias Beck | q-chromatic polynomials | Zoom link | ||
| 11:00 - 11:30 | Ice breakers | Zoom link | |||
| 11:30 - noon | Ezgi Kantarcı Oğuz | TBA | Zoom link | ||
| noon - 1:30 | Lunch and poster session A | Gather link | |||
| 1:30 - 2:00 | Vasu Tewari | TBA | Zoom link | ||
| 2:00 - 2:30 | Critter time | Zoom link | |||
| 2:30 - 3:00 | José Aliste-Prieto | Counting subtrees with the Chromatic symmetric function | Zoom link | ||
| 3:00 - 4:00 | Puzzles | Zoom link | |||
| 4:00 - 4:30 | Anna Pun | Combinatorial identities for vacillating tableaux | Zoom link | ||
| 4:30 - 5:00 | Coffee break | Gather link | |||
| 5:00 - 5:30 | Dominic Searles | TBA | Zoom link | ||
| 5:30 - 6:00 | Happy hour | Gather link |
JUNE 18 (TUESDAY):
| 10:00 - 10:30 AM | Welcome | Gather link | |||
| 10:30 - 11:00 | Eric Marberg | TBA | Zoom link | ||
| 11:00 - 11:30 | AlCoVE art time | Zoom link | |||
| 11:30 - noon | Sarah Brauner | TBA | Zoom link | ||
| noon - 1:30 PM | Lunch and poster session B | Gather link | |||
| 1:30 - 2:00 | Greta Panova | TBA | Zoom link | ||
| 2:00 - 2:30 | Virtual expedition | Zoom link | |||
| 2:30 - 3:00 | Kris Shaw | TBA | Zoom link | ||
| 3:00 - 4:00 | Puzzles | Zoom link | |||
| 4:00 - 4:30 | Christian Gaetz | TBA | Zoom link | ||
| 4:30 - 5:00 | Coffee break | Gather link | |||
| 5:00 - 5:30 | Sam Hopkins | Upho posets | Zoom link | ||
| 5:30 - 6:00 | Happy hour | Gather link |
Abstracts of talks and posters
José Aliste-Prieto
Counting subtrees with the Chromatic symmetric function
Richard Stanley asked in 1995 whether a tree is determined up to isomorphism by its chromatic symmetric function. One approach to understanding this question is to ask which other invariants are encoded by the chromatic symmetric function: Here we consider two invariants: The subtree polynomial, which counts subtrees by cardinality and number of leaves, and the generalized degree sequence, which counts vertex subsets by cardinality, number of internal and external edges. In 2008, Jeremy Martin, Mathew Morin and Jennifer Wagner proved that the chromatic symmetric function determines the subtree polynomial, while Crew Conjecture states that the chromatic symmetric function also determines the generalized degree sequence.
In this work, we first prove Crew’s conjecture, and then show that a restriction of the generalized degree sequence contains the same information as the subtree polynomial. Finally, we will show recurrences for the restriction of the generalized degree sequence that allow us to construct arbitrarily large families of trees sharing the same subtree polynomials, proving and generalizing a conjecture of Eisenstat and Gordon.
This is joint work with Jeremy L. Martin, Jennifer Wagner, and José Zamora.
Matthias Beck
q-chromatic polynomials
We introduce and study a q-version of the chromatic polynomial of a given graph G, defined as the sum of \(q^{l*c(v)}\) where \(l\) is a fixed integral linear form and the sum is over all proper n-colorings \(c\) of G. This turns out to be a polynomial in the q-integer \([n]_q\), with coefficients that are rational functions in q. We will exhibit several other structural results for q-chromatic polynomials, as well as connections to neighboring concepts, e.g., chromatic symmetric functions and the arithmetic of order polytopes. We offer a strengthened version of Stanley's conjecture that the chromatic symmetric function distinguishes trees, which leads to an analogue of P-partitions for graphs. This is joint work with Esme Bajo and Andrés Vindas-Meléndez.
Sam Hopkins
Upho posets
A partially ordered set is called upper homogeneous, or "upho," if every principal order filter is isomorphic to the whole poset. This class of fractal-like posets was recently introduced by Stanley. Our first observation is that the rank generating function of a (finite type \(\mathbb{N}\)-graded) upho poset is the reciprocal of its characteristic generating function. This means that each upho lattice has associated to it a finite graded lattice, called its core, that determines its rank generating function. With an eye towards classifying upho lattices, we investigate which finite graded lattices arise as cores, providing both positive and negative results. Our overall goal for this talk is to advertise upho posets, and especially upho lattices, which we believe are a natural and rich class of posets deserving of further attention.
Anna Pun
Combinatorial identities for vacillating tableaux
Vacillating tableaux, which are sequences of integer partitions that satisfy specific conditions, arise in the representation theory of the partition algebra and the combinatorial theory of crossings and nestings of matchings and set partitions. By exploring a correspondence between vacillating tableaux and pairs comprising a set partition and a partial Young tableau, we derive combinatorial identities that involve the number of vacillating tableaux, the number of standard Young tableaux and Schur functions.
In this talk, we will define vacillating tableaux and explore their correspondence with pairs of set partitions and partial Young tableaux. This correspondence will be used to derive combinatorial identities involving the number of vacillating tableaux, standard Young tableaux, and Schur functions. We will also discuss integer sequences that count associated combinatorial structures. This is a joint work with Zhanar Berikkyzy, Pamela E. Harris, Catherine Yan and Chenchen Zhao.