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math.CO2026
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…
math.CO2026
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…
math.CO2026
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…