Combinatorics Seminar

The Fall 2025 Combinatorics seminar is organized by Miklos Bona

It meets Tuesdays P8 (3:00-3:50) in LIT 225.

Date	Speaker	Title	Abstract
9/2	Miklos Bona	Stack-sorting preimages and 0-1-trees	We define a class of partially labeled trees and use them to find simple proofs for two recent enumeration results of Colin Defant concerning
9/9	Jack Chou	Newton polytopes of fireworks Grothendieck polynomials	We show that the support of a Grothendieck polynomial $\mathfrak G_w$ of any fireworks permutation is as large as possible: a monomial appears in $\mathfrak G_w$ if and only if it divides $\mathbf x^{\mathrm{wt}(\overline{D(w)})}$ and is divisible by some monomial appearing in the Schubert polynomial $\mathfrak S_w$. Our formula implies that the homogenization of $\mathfrak G_w$ has M-convex support. We also show that for any fireworks permutation $w$, there exists a layered permutation $\pi(w)$ so that $\mathrm{supp}(\mathfrak G_{\pi(w)})\supseteq \mathrm{supp}(\mathfrak G_w)$. This is joint work with Linus Setiabrata.
9/16
9/23
9/30	Michael Waite	Permutations containing r copies of 321	We will show that the generating function for permutations containing r copies of a 321 pattern is not a rational function. We will then show how to generalize our approach in order to prove a similar result for longer monotone patterns.
10/7
10/14	Andrew Vince	A Conjecture on Connected Subgroups of a Graph
10/21
10/28
11/4
11/11
11/18 (Rescheduled to January)	Nolan Ison	Zero Forcing on 2-connected Outerplanar Graphs	Zero Forcing is an `infection' game played on graphs. We start with a subset of vertices, S, that is infected. There is one forcing rule, namely, if u is an infected vertex and exactly one neighbor v of u is not infected, then v becomes infected. We say that u forces v. We call S a Zero Forcing Set in G if every vertex of G eventually becomes infected. A natural question is the following: What is the minimum cardinality of a zero forcing set? In other words, what is the smallest number of originally infected vertices that will end up infecting the entire graph?
12/2	Nicholas Van Nimwegen	Almost distant monotone patterns	In a previous work, Bóna and Pantone studied permutations that avoided all but one pattern of length k that began with a length k-1 increasing subsequence. We draw the connection between that idea and distant patterns, and study similar permutation classes where the index not part of the increasing subsequence can vary. We find a large class of Wilf-Equivalences between k+1 classes of k patterns of length k+1, and outline several classes of unbalanced Wilf-Equivalences related to the first class. Using this, we are also find new bounds on the exponential growth rate on all monotone distant patterns with a single gap constraint.