Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...

Abstract: We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified ...

The field of functional analysis of symmetric analytic functions explores the interplay between the structure of analytic function algebras and the inherent symmetries dictated by invariance under ...

Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can ...

We use the boson-fermion correspondence for S and Q functions to establish some interesting properties concerning outer products and plethysms of S-functions (or Q-functions) by power sum symmetric ...

Notifications You must be signed in to change notification settings As part of the discrete math exam revision, Coder Academy issued some optional Python challenges to consolidate our understanding of ...

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It is well-known that any Boolean function f:-1,+1 n to -1,+1 can be written uniquely as a polynomial f(x) = sum S subset [n] f s prod i in S x i. The collection of coefficients (f S ‘s) this ...

\begin{equation*}\;s_{{\lambda}}({\bar {x}})=\frac{{\mathrm{det}}{\parallel}x_{i}^{n-j+{\lambda}_{j}}{\parallel}_{i,j=1}^{n}}{{\mathrm{det}}{\parallel}x_{i}^{n-j ...