| Talk_id | Date | Speaker | Title |
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31525
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Wednesday 1/25
3:00 PM
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Yibo Gao, University of Michigan
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CANCELLED: Symmetric structures in the strong Bruhat order
- Yibo Gao, University of Michigan
- CANCELLED: Symmetric structures in the strong Bruhat order
- 01/25/2023
- 3:00 PM - 3:50 PM
- C304 Wells Hall
- Bruce E Sagan (bsagan@msu.edu)
The Bruhat order encodes algebraic and topological information of Schubert varieties in the flag manifold and possesses rich combinatorial properties. In this talk, we discuss three interrelated stories regarding the Bruhat order: self-dual Bruhat intervals, Billey-Postnikov decompositions and automorphisms of the Bruhat graph. This is joint work with Christian Gaetz.
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31557
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Wednesday 2/1
3:00 PM
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Stephen Lacina, University of Oregon
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Maximal Chain Descent Orders
- Stephen Lacina, University of Oregon
- Maximal Chain Descent Orders
- 02/01/2023
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Bruce E Sagan (bsagan@msu.edu)
We introduce a new partial order called the maximal chain descent order on the maximal chains of any finite, bounded poset with an EL-labeling. We prove that the maximal chain descent order encodes via its linear extensions all shellings of the order complex induced by the EL-labeling strictly including the well-known lexicographic shellings. We show that the standard EL-labeling of the Boolean lattice has maximal chain descent order isomorphic to the type A weak order. We also prove that natural EL-labelings of intervals in Young's lattice give maximal chain descent orders isomorphic to partial orders on the standard Young tableaux or standard skew tableaux of a fixed shape given by swapping certain entries. We additionally show that the cover relations of maximal chain descent orders are generally more subtle than one might first expect, but we characterize the EL-labelings with the expected cover relations including many well-known families of EL-labelings.
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31563
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Wednesday 2/8
3:00 PM
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Wenjie Fang, Graz University of Technology
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Parabolic Tamari Lattices in Linear Type B
- Wenjie Fang, Graz University of Technology
- Parabolic Tamari Lattices in Linear Type B
- 02/08/2023
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Bruce E Sagan (bsagan@msu.edu)
We study parabolic aligned elements associated with the type-B Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the type-B case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the type-B Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the type-B analogue of the parabolic Tamari lattice introduced for type A in (Mühle and Williams, 2019). These lattices have not appeared in the literature before. As work in progress, we will also talk about various combinatorial models and bijections between them. Joint work with Henri Mühle and Jean-Christophe Novelli.
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