6 citations · 11 across the 5 of their papers we have counts for
5 papers
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…
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…
On 3 and 4 dimensional regular solids, Part 1: The 4-simplex generates the free group
Adrian Ocneanu
The 4-simplex has vertices 5 unit quaternions, which we arrange so that one of them is the unit. We show that the remaining 4 vertices are the generators of a free group. For the p…
On the inner structure of a permutation: Bicolored Partitions and Eulerians, Trees and Primitives
Adrian Ocneanu
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of…
A note on simplicial dimension shifting
Adrian Ocneanu
We discuss a simplicial dimension shift which associates to each n-manifold an n-1-manifold. As a corollary we show that an invariant which was recently proposed by Ooguri and by C…