Brandeis Combinatorics Seminar -  Spring 2026

The Brandeis Combinatorics Seminar is an introductory seminar for combinatorics.
The talks should be (at least partially) understandable to first year graduate students.

            The zoom link is  https://brandeis.zoom.us/j/98465451178 (only for talks marked as on Zoom). 

February 9:  (In Person)

Speaker: Neha Goregaokar (Brandeis)

Title:  Equitable coloring of random graphs

Abstract: This talk will be based on the paper Equitable colorings of random graphs by Michael Krivelevich and Balázs Patkós. The talk will cover equitable chromatic numbers and thresholds as well as some results about their asymptotic behavior.

March 2: (On Zoom)

Speaker: Ananth Ravi (TU Delft)

Title:  The chromatic number of finite projective spaces

Abstract: The chromatic number of the finite projective space PG(n−1,q), denoted χ_q(n), is the minimum number of colors needed to color its points so that no line is monochromatic. We establish a new recursive bound, and using this recursion, we obtain new upper bounds on χ_q(n) for all q.

For q = 2, we refine the recursion and prove that χ_2(n) ≤ ⌊2n/3⌋ + 1 for all n ≥ 2, and that this bound is tight for all n ≤ 7. This recovers all previously known cases for n ≤ 6 and resolves the first open case n = 7. 

We also make connections to the multicolor Ramsey numbers for triangles and multicolor vector-space Ramsey numbers.

This work is in collaboration with Anurag Bishnoi and Wouter Cames van Batenburg. Here is the arXiv link to the paper: https://arxiv.org/abs/2512.01760.

April 13: (In person)

Speaker: Dale R. Worley

Title:  Representation of locally-finite distributive lattices

Abstract: Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.  Stone has generalized the representation theorem to all distributive lattices, but the generalization uses topological machinery that is complex to apply to discrete lattices.

We present a simpler extension to general distributive lattices.  We then apply this formulation to locally-finite distributive lattices to produce a novel representation theorem:  The lattice is isomorphic to a sublattice of the order ideals of the poset of prime filters of the lattice whose symmetric difference from a particular ideal is finite.  This sublattice is one connected component of the lattice of all such ideals when its Hasse diagram is viewed as a graph.  We present a conjecture regarding when this sublattice is the entirety of the lattice of order ideals, except possibly disconnected top and bottom elements.

April 20:  (In person)

Speaker: Elsa Frankel (Wellesley College)

Title:  Lattices from a Curious Game on Partitions

Abstract: Hyperbinary partitions are integer partitions with all parts as powers of two, with multiplicities of at most two. Recently McConville, Propp, and Sagan showed that posets of hyperbinary partitions, under refinement ordering, are distributive lattices. We will discuss a generalization to hyper (b, t)-ary partitions, which have parts as powers of b, with multiplicities of at most t. Namely, we find that posets of hyper (b, t)-ary partitions, under refinement ordering, are also distributive lattices. Much also remains to be explored in the hyperbinary case, and we will share a bijection with lattices of perfect matchings on snake graphs, which arise from ideas in cluster algebra theory. 

April 27: (In person)

Speaker: Neha Goregaokar (Brandeis University)

Title:  Bijectivity of a generalized Pak-Stanley labeling

Abstract: The Pak-Stanley labeling is a bijection between the regions of the $m$-Shi arrangement and the $m$-parking functions. Mazin generalized this labeling to every deformation of the braid arrangement and proved that this labeling is always surjective onto a set of directed multigraph parking functions. We provide a right inverse to the generalized Pak-Stanley labeling, and identify a class $\mathcal{C}$ of arrangements for which this labeling is bijective. The class $\mathcal{C}$ includes the multi-Shi arrangements and the multi-Catalan arrangements. We also show that the arrangements in $\mathcal{C}$ are the only transitive arrangements for which the generalized Pak-Stanley labeling is bijective. This is joint work with Olivier Bernardi. 

Links to previous semesters: Fall2025, Spring2025 Fall2024, Spring2024, Fall2023, Spring2023, Fall 2022, Spring 2022, Fall 2021, Spring 2020, Fall 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013.