Recent advances in the study of automorphism groups within graph theory have yielded significant theoretical and applied insights. At its core, the interplay between the algebraic structure of groups ...

Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can ...

Abstract: We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant ...

Abstract: We propose a graph automorphism-based algorithm for computing maximal sets of symmetric inputs of circuits. It can be used to identify nonsymmetric inputs in a circuit and enhance the ...

Algebraic varieties and their automorphism groups lie at the heart of modern algebraic geometry, intertwining deep theoretical concepts with practical applications. Algebraic varieties, defined as the ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

If AG is a finite solvable group with (|A|, |G|) = 1 and $G \triangleleft AG$, we explore the relationship between the Fitting height of G, the composition length of ...

Can check if graphs are isomorphic, or count automorphisms of graphs. Uses advanced techniques such as the orbit-stabilizer theorem, Hopcroft's DFA minimization, and preprocessing of twins and tree ...