6 citations · 19 across the 7 of their papers we have counts for
7 papers
Characteristic elements for real hyperplane arrangements
Marcelo Aguiar, Jose Bastidas, Swapneel Mahajan
Characteristic elements of the Tits algebra of a real hyperplane arrangement carry information about the characteristic polynomial. We present this notion and its basic properties,…
Hopf monoids in the category of species
Marcelo Aguiar, Swapneel Mahajan
A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained introduction to the theory of Hopf monoids in t…
On the Hadamard product of Hopf monoids
Marcelo Aguiar, Swapneel Mahajan
Combinatorial structures which compose and decompose give rise to Hopf monoids in Joyal's category of species. The Hadamard product of two Hopf monoids is another Hopf monoid. We p…
Symplectic operad geometry and graph homology
Swapneel Mahajan
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and…
The cd-index of the Boolean lattice
Swapneel Mahajan
We study some properties of the {\bf cd}-index of the Boolean lattice. They are extremely similar to the properties of the {\ab}-index, or equivalently, the flag -vector of the…
Projections, shellings and duality
Swapneel Mahajan
Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bj{ö}rner. In this paper…