Combinatorics and physics Combinatorics and physics Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. "Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory.". "Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics". Combinatorics has always played an important role in quantum field theory and statistical physics. However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer, showing that the renormalization of Feynman diagrams can be described by a Hopf algebra. Combinatorial
Interaction technique line and direct manipulation user interfaces. While interaction techniques are typically technology-, platform-, and/or implementation-dependent (see #level of granularity above), human-computer or human-information interactions can be characterized at higher levels of abstraction that are independent of particular technologies and platforms. At such levels of abstraction, the concern is not precisely how an interaction is performed; rather, the concern is a conceptual characterization of what the interaction is, and what the general utility of the interaction is for the user(s). Thus, any single interaction pattern may be instantiated by any number of interaction techniques, on any number of different technologies and