seminars:comb:start
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seminars:comb:start [2026/02/03 10:42] zaslav [SPRING 2026] |
seminars:comb:start [2026/02/10 16:09] (current) laura |
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| **Tuesday, 2/10**\\ | **Tuesday, 2/10**\\ | ||
| Speaker: Tan Tran (Binghamton)\\ | Speaker: Tan Tran (Binghamton)\\ | ||
| - | Title: \\ | + | Title: Signatures in Type A Root Systems and Eulerian Numbers\\ |
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
| Location: WH 100E | Location: WH 100E | ||
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| + | Let $\Phi$ be a type A root system of rank $n$. In this talk, I introduce a combinatorial invariant, called a "signature", associated with subsets of $n+1$ positive roots. Given such a subset, its signature records the numbers of positive and negative values among certain determinants obtained by deleting one root at a time. The main construction can be formulated using only elementary linear algebra. | ||
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| + | We show that the number of subsets with a given signature can be expressed explicitly in terms of the classical Eulerian numbers. While connections between root systems and Eulerian numbers are well known, this result gives another interpretation of Eulerian numbers in terms of determinant data arising in type A. | ||
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| + | These signatures are motivated by questions coming from hyperplane arrangements associated with $\Phi$, including the Shi, Catalan, Linial, and Ish arrangements. As applications, we compute the minimum period of the characteristic quasi-polynomial of these arrangements and determine the values of both the classical and arithmetic Tutte polynomials at (1,1). | ||
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| + | This is joint work with M. Cuntz (Hannover), H.M. Tran (Hanoi), and S. Tsujie (Hokkaido). | ||
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| **Tuesday, 3/3**\\ | **Tuesday, 3/3**\\ | ||
| - | Speaker: \\ | + | Speaker: Thomas Galvin (Binghamton)\\ |
| Title: \\ | Title: \\ | ||
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
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| **Tuesday, 3/24**\\ | **Tuesday, 3/24**\\ | ||
| - | Speaker: \\ | + | Speaker: Thomas Martinez (UCLA and Cornell) \\ |
| Title: \\ | Title: \\ | ||
| Time: 1:30-2:30\\ | Time: 1:30-2:30\\ | ||
seminars/comb/start.1770133377.txt · Last modified: 2026/02/03 10:42 by zaslav