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We introduce a supersymmetric analog of the classical Coxeter frieze patterns. Our approach is based on the relation with linear difference operators. We define supersymmetric analogs of linear difference operators called Hills operators. The space of these superfriezes is an algebraic supervariety, which is isomorphic to the space of supersymmetric second order difference equations, called Hills equations.
We introduce a new class of friezes which is related to symplectic geometry. On the algebraic and combinatrics sides, this variant of friezes is related to the cluster algebras involving the Dynkin diagrams of type ${rm C}_{2}$ and ${rm A}_{m}$. On t
Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the equivariant
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents
Riordan matrices are infinite lower triangular matrices determined by a pair of formal power series over the real or complex field. These matrices have been mainly studied as combinatorial objects with an emphasis placed on the algebraic or combinato
Frieze patterns of numbers, introduced in the early 70s by Coxeter, are currently attracting much interest due to connections with the recent theory of cluster algebras. The present paper aims to review the original work of Coxeter and the new develo