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Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative
4 videos

Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints
3 videos

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Not Only Scalar Curvature Seminar
60 videos

Not Only Scalar Curvature Seminar

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
4 videos

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models

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Combinatorics and Arithmetic for Physics: special days 2023

Collection Combinatorics and Arithmetic for Physics: special days 2023

Organizer(s) Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON
Date(s) 15/11/2023 - 17/11/2023
linked URL https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
00:00:00 / 00:00:00
18 27

The Redei–Berge symmetric function of a directed graph

By Darij Grinberg

In 1934, Laszlo Redei observed a peculiar property of tournaments (directed graphs that have an arc between every pair of distinct vertices): Each tournament has an odd number of Hamiltonian paths. In 1996, Chow introduced the “path-cycle symmetric function” of a directed graph, a symmetric function in two sets of arguments, which was later used in rook theory. We study Chow’s symmetric function in the case when the y-variables are 0. In this case, we give new nontrivial expansions of the function in terms of the power-sum basis; in particular, we find that it is p-positive as long as the directed graph has no 2-cycles. We use our expansions to reprove Redei’s theorem and refine it to a mod-4 congruence. Joint work with with Richard P. Stanley.

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  • Date of publication 22/11/2023
  • Institution IHES
  • Audience Researchers
  • Format MP4

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