Talk_id  Date  Speaker  Title 
29391

Thursday 9/8 3:00 PM

Lara Pudwell, Valparaiso University

Patternavoiding parking functions
 Lara Pudwell, Valparaiso University
 Patternavoiding parking functions
 09/08/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We extend the classical definition of patterns in permutations to parking functions. In particular we study parking functions that avoid permutations of length 3. A number of wellknown combinatorial sequences arise in our analysis, and this talk will highlight several bijective results. This project is joint work with Ayomikun Adeniran.

29410

Wednesday 9/14 3:00 PM

Brendon Rhoades, UCSD

Superspace, Vandermondes, and representations
 Brendon Rhoades, UCSD
 Superspace, Vandermondes, and representations
 09/14/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We present an extension of the Vandermonde determinant from the polynomial ring to superspace. These superspace Vandermondes are used to construct modules over the symmetric group with (occasionally conjectural) connections to geometry and coinvariant theory. Joint with Andy Wilson.

29416

Wednesday 9/21 3:00 PM

Alex Wilson, Dartmouth

A DiagramLike Basis for the Multiset Partition Algebra
 Alex Wilson, Dartmouth
 A DiagramLike Basis for the Multiset Partition Algebra
 09/21/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
There's a classical connection between the representation theory of the symmetric group and the general linear group called SchurWeyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset partition algebra. The partition algebra has a wellknown basis indexed by graphtheoretic diagrams which allows the multiplication in the algebra to be understood visually as combinations of these diagrams. I will present an analogous basis for the multiset partition algebra and show how this basis can be used to describe generators and construct representations for the algebra.

29429

Wednesday 9/28 3:00 PM

Ayomikun Adeniran, Colby College

Parking completions
 Ayomikun Adeniran, Colby College
 Parking completions
 09/28/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Parking functions are wellknown objects in combinatorics. One interesting generalization of parking functions are parking completions. A parking completion corresponds to a set of preferences where all cars park assuming some of the spots on the street are already occupied. In this talk, we will explore how parking completions are related to restricted lattice paths. We will also present results for both the ordered and unordered variations of the problem by use of a pair of operations (termed Join and Split). A nice consequence of our results is a new volume formula for most PitmanStanley polytopes. This is joint work with H. Nam, P.E. Harris, G. DorpalenBarry, S. Butler, J.L. Martin, C. Hettle, and Q. Liang.

29446

Wednesday 10/5 3:00 PM

Caroline Klivans, Brown University

Flowfiring processes
 Caroline Klivans, Brown University
 Flowfiring processes
 10/05/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
I will discuss a discrete nondeterministic flowfiring process for topological cell complexes. The process is a form of discrete diffusion; a flow is repeatedly diverted according to a discrete Laplacian. The process is also an instance of higherdimensional chipfiring. I will motivate and introduce the system and then focus on two important features – whether or not the system is terminating and whether or not the system is confluent.

29447

Thursday 10/13 3:00 PM

Patricia Hersh, University of Oregon

Generalized recursive atom ordering and equivalence to CLshellability
 Patricia Hersh, University of Oregon
 Generalized recursive atom ordering and equivalence to CLshellability
 10/13/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
When Björner and Wachs introduced one of the main forms of lexicographic shellability, namely CLshellability, they also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CLshellable if and only if it admits a recursive atom ordering. We generalize the notion of recursive atom ordering, and we prove that any such generalized recursive atom ordering may be transformed via a reordering process into a recursive atom ordering. We also prove that a finite bounded poset admits a generalized recursive atom ordering if and only if it is ``CCshellable'' by way of a CClabeling which is selfconsistent in a certain sense. This allows us to conclude that CLshellability is equivalent to selfconsistent CCshellability. As an application, we prove that the uncrossing orders, namely the face posets for stratified spaces of planar electrical networks, are dual CLshellable.
During this talk, we will review plenty of background on poset topology and specifically regarding the technique of lexicographic shellability. This is joint work with Grace Stadnyk

30468

Wednesday 10/26 3:00 PM

Nadia Lafrenière, Dartmouth

A Study Of Homomesy On Permutations Using The FindStat Database
 Nadia Lafrenière, Dartmouth
 A Study Of Homomesy On Permutations Using The FindStat Database
 10/26/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We performed a systematic study of permutation statistics and
bijective maps on permutations, looking for the homomesy phenomenon.
Homomesy occurs when the average value of a statistic is the same on
each orbit of a given map. The maps that exhibit homomesy include the
Lehmer code rotation, the reverse, the complement, and the
Kreweras complement, all of which have some geometric interpretations.
The statistics studied relate to familiar notions such as inversions,
descents, and permutation patterns, among others. Beside the many new
homomesy results, I’ll discuss our research method, in which we used
SageMath to search the FindStat combinatorial statistics database to
identify potential instances of homomesy, and what this experiment
taught us about the maps themselves and the homomesy phenomenon at large.
This is joint work with Jennifer Elder, Erin McNicholas, Jessica Striker
and Amanda Welch.

30478

Wednesday 11/2 3:00 PM

James Propp, University of Massachusetts, Lowell

A Pentagonal Number Theorem for Tribone Tilings
 James Propp, University of Massachusetts, Lowell
 A Pentagonal Number Theorem for Tribone Tilings
 11/02/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Conway and Lagarias used combinatorial group theory to show that certain
roughly triangular regions in the hexagonal grid cannot be tiled by the
shapes Thurston later dubbed tribones. The ideas of Conway, Lagarias, and
Thurston have found many applications in the study of tilings in the plane.
Today I'll discuss a twoparameter family of roughly hexagonal regions in
the hexagonal grid I call benzels. A variant of Gauss’ shoelace formula
allows one to compute the signed area (aka algebraic area) enclosed by a
closed polygonal path, and by “twisting” the formula one can compute the
values of the ConwayLagarias invariant for all benzels. It emerges that the
(a,b)benzel can be tiled by tribones if and only if a and b are the paired
pentagonal numbers k(3k+1)/2, k(3k1)/2. This is joint work with Jesse Kim.

30497

Wednesday 11/16 3:00 PM

John Shareshian, Washington University

Coset lattices, invariable generation of simple groups, and a problem on binomial coefficients
 John Shareshian, Washington University
 Coset lattices, invariable generation of simple groups, and a problem on binomial coefficients
 11/16/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
In joint work with Russ Woodroofe, we showed that the order complex of the poset of all cosets of all proper subgroups of a finite group, ordered by inclusion, has noncontractible order complex using Smith Theory. A key part of our proof involves invariable generation of finite groups: two subsets $S,T$ of a group $G$ generate $G$ invariably if, for every $g,h \in G$, $g^{1}Sg$ and $h^{1}Th$ together generate $G$. It remains open whether the alternating group $A_n$ can be generated invariably by $\{s\}$ and $\{t\}$ with both $s,t$ having prime power order. This question is closely related to a (still open) question about prime divisors of binomial coefficients. I will discuss all of this, along with current work joint with Bob Guralnick and Russ Woodroofe about invariable generation of arbitrary simple groups by two elements of prime or prime power order.

31503

Wednesday 11/30 3:00 PM

Laura Hernando Colmenarejo, North Carolina State University

Multiplying quantum Schubert polynomials using combinatorics
 Laura Hernando Colmenarejo, North Carolina State University
 Multiplying quantum Schubert polynomials using combinatorics
 11/30/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Schubert polynomials are a very interesting family of polynomials in algebraic geometry due to their relation with the cohomology of the flag variety. Moreover, they are also very interesting from a combinatorial point of view because they can be considered generalizations of Schur functions. In this talk, we will talk about how to multiply a Schubert polynomial by a Schur function indexed by a hook and how we can extend this multiplication to the quantum world. This is a current work with C. Benedetti, N. Bergeron, F. Saliola, and F. Sottile.

31507

Wednesday 12/7 3:00 PM

Jinting Liang, Michigan State University

Enriched toric $[\vec{D}]$partitions
 Jinting Liang, Michigan State University
 Enriched toric $[\vec{D}]$partitions
 12/07/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
In this talk I will discuss the theory of enriched toric $[\vec{D}]$partitions. Whereas Stembridge's enriched $P$partitions give rises to the peak algebra which is a subring of the ring of quasisymmetric functions QSym, our enriched toric $[\vec{D}]$partitions will generate the cyclic peak algebra which is a subring of cyclic quasisymmetric functions cQSym. In the same manner as the peak set of linear permutations appears when considering enriched $P$partitions, the cyclic peak set of cyclic permutations plays an important role in our theory.
