4 papers · 1 filter
The radial derivative on the graded Möbius algebra
Thomas Sinclair
Let be a simple matroid and let be the graded Möbius algebra of its lattice of flats. The ordered-basis weights of flats define an inner product for which the adjoints o…
Finite free convolution via reproducing kernels and squarefree algebras
Thomas Sinclair
We give a structural account of the finite free convolutions of Marcus, Spielman, and Srivastava in terms of reproducing kernel inner products on polynomial spaces and a multilinea…
An operator-theory construction on geometric lattices
Thomas Sinclair
We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives r…
The model theory of metric lattices: pseudofinite partition lattices
José Contreras Mantilla, Jose Contreras-Mantilla, Thomas Sinclair
We initiate the study of general metric lattices in the context of the model theory of metric structures. As an application we develop a theory of pseudo-finite limits of partition…