2025 CMS Summer Meeting
Quebec City, June 6 - 9, 2025
Combinatoire algébrique et énumérative
Org: Samuele Giraudo and Jose Dario Bastidas Olaya (Université du Québec à Montréal)
[PDF]
Org: Samuele Giraudo and Jose Dario Bastidas Olaya (Université du Québec à Montréal)
[PDF]
- ANTOINE ABRAM, Université du Québec à Montréal
- SPENCER BACKMAN, University of Vermont
- NANTEL BERGERON, bergeron@yorku.ca
Vine model for double forest polynomials [PDF]
- SPENCER BACKMAN, University of Vermont
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Together with Lucas Gagnon, Philippe Nadeau, Hunter Spink, and Vasu Tewari, we introduced double forest polynomials in our study of equivariant quasisymmetric functions and their connections to geometry. In this talk, I will discuss the vine model, which provides a framework for computing double forest polynomials.
- ELISABETH BULLOCK, Massachusetts Institute of Technology
Ehrhart series of alcoved polytopes [PDF]
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In this talk (based on joint work with Yuhan Jiang), I will describe a general method for computing the Ehrhart series of any alcoved polytope via a particular shelling order of its alcoves. As an application, we get a bijective proof of the formula for the Ehrhart h*-polynomial of the second hypersimplex $\Delta_{2,n}$ in terms of Nick Early’s decorated ordered set partitions.
- ANGELA CARNEVALE, University of Galway
- SERGI ELIZALDE, Dartmouth
A bijection for descent sets of permutations with only even and only odd cycles [PDF]
- SERGI ELIZALDE, Dartmouth
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It is known that, when $n$ is even, the number of permutations of $\{1,2,\dots,n\}$ all of whose cycles have odd length equals the number of those all of whose cycles have even length.
Adin, Hegedűs and Roichman recently found a surprising refinement of this equality, showing that it still holds when restricting to permutations with a given descent set $J$ on one side, and permutations with ascent set $J$ on the other. Their proof is algebraic and relies on higher Lie characters. It also yields a version for odd $n$.
In this talk we give a bijective proof of the refined identity. First, using known bijections of Gessel, Reutenauer and others, we restate it in terms of multisets of necklaces, which we interpret as words. Then, we construct a weight-preserving bijection between words all of whose Lyndon factors have odd length and are distinct, and words all of whose Lyndon factors have even length.
- ALEJANDRO GALVAN, Dartmouth College
- YAN LANCIAULT, Université du Québec à Montréal
- GAYEE PARK, Dartmouth College
Naruse hook formula for mobile posets [PDF]
- YAN LANCIAULT, Université du Québec à Montréal
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Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like Young diagrams of straight shapes and $d$-complete posets have hook-length product formulas to count linear extensions, whereas families like Young diagrams of skew shapes have determinant or positive sum formulas like the Naruse hook-length formula from 2014. In 2020, Garver et. al. gave determinant formulas to count linear extensions of a family of posets called mobile posets that refine $d$-complete posets and border strip skew shapes. We give a Naruse type hook-length formula to count linear extensions of such posets by proving a major index $q$-analogue. We also give an inversion index $q$-analogue of the Naruse formula for mobile tree posets.
- SASHA PEVZNER, Northeastern University
- COLLEEN ROBICHAUX, UCLA
Signed puzzles for Schubert coefficients [PDF]
- COLLEEN ROBICHAUX, UCLA
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We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of a recurrence of Knutson. We use the rule to prove polynomiality of the sums of Schubert coefficients with bounded number of inversions. This is joint work with Igor Pak.
- ANDREW SACK, University of Michigan
- KARTIK SINGH, University of Waterloo
- HUNTER SPINK, University of Toronto
- TIANYI YU, Université du Québec à Montréal
- KARTIK SINGH, University of Waterloo