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math.CO2022
Braid arrangement bimonoids and the toric variety of the permutohedron
William Norledge
We show that the toric variety of the permutohedron (=permutohedral space) has the structure of a cocommutative bimonoid in species, with multiplication/comultiplication given by e…
math.CO2019
Hopf monoids, permutohedral cones, and generalized retarded functions
William Norledge, Adrian Ocneanu
The commutative Hopf monoid of set compositions is a fundamental Hopf monoid internal to vector species, having undecorated bosonic Fock space the combinatorial Hopf algebra of qua…
math.CO2019★ 6 cited
The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations
Zhengwei Liu, William Norledge, Adrian Ocneanu
We study a certain discrete differentiation of piecewise-constant functions on the adjoint of the braid hyperplane arrangement, defined by taking finite-differences across hyperpla…