Combined arms is a military theory thing that resembles rock-scissor-paper a bit: One part of the mix trumps when the others don't succeed. Some advanced theorizing about combined arms talks of dislocating enemy strengths, while more doctrine-oriented theorizing raises combined arms to a golden rule for force composition. Combined arms doesn't always have the same meaning, though.
Combined arms on an ancient battlefield would mean heavy infantry, missile troops (bowmen, slingers, javelineers) and cavalry (substituted for by light infantry in horses-poor regions).
Combined arms on a European 17th century battlefield would mean pikemen, musketeers, cavalry and artillery.
Combined arms on a European 18th century battlefield was no doubt infantry, artillery and cavalry (the bayonet had joined musketeers with pikemen).
Combined arms in a WW2 sea battle could be escorts (DD/DE/CLAA), armoured gunfighter ships (BB/BC/CA/CL) and aircraft carriers (CV/CVL/CVE/CVS).
Combined arms in a modern air force strike package could be fighters, bombers, SEAD (suppression of enemy air defences) specialist aircraft and stand-off jammer (radio and radar) aircraft.
Combined arms on a modern battlefield would usually be defined as armour, infantry and artillery (including mortars for this purpose).
This is where I tend to disagree. The list already shows that technological development may change the meaning of combined arms; the meaning is not carved in stone.
It is rather likely that combat engineers should be recognised as a worthy component of combined arms; they are a supporting branch, but they do what combine arms is about: Be the ace in the hole that leads to success when the other branches don't succeed.
Another component that deserves attention -especially at these times- is battlefield air defence, possibly in union with C-RAM (counter rocket artillery mortar (munitions)). Battlefield air defences are necessary in face of aerial drones, but too many people still think that we need little or no battlefield air defences because of our oh-so great fighter fleets.
Modern warfare is very sophisticated and it shouldn't surprise that modern combined arms should have more components than the ancient one.
Here's yet another component; electronic warfare. This comes almost straight out of university physics departments. The physics behind electromagnetic stuff are really tricky, and EW is mostly about exactly this stuff.
Back during the 17th century a line of pikemen in front of the musketeers usually broke up a cavalry charge without actual fighting - a charge into an orderly line of pikes was stupid. Nowadays the well-timed and correct application of a radio jammer could break up a tank company attacking movement because tanks without radio comm would be at a severe disadvantage (example).
Finally I would claim that reconnaissance and observer troops deserve a place of their own, but that's a long story.
Three of these are embodiments of military power. A matchup of army forces for public information would count personnel (kind of representing infantry), main battle tanks (or AFVs in general) and artillery pieces (usually ignoring mortars). Some such inter-military matchups also add air power elements such as combat aircraft and battlefield helicopters.
The others - combat engineers, air defences, electronic warfare - don't appear in such matchups, and that's symptomatic of how they get a lot less attention. This doesn't hurt much unless the budget gets rigged for style over substance (overemphasising armour, infantry and artillery) or unless doctrine neglects some combined arms elements. There's usually a field manual for everything, so total doctrinal neglect is unlikely, but one might still be concerned over infantry battalion field manuals paying no or almost no attention to the cooperation with electronic warfare troops or combat engineers, for example.
I have to admit I didn't find a single military theory work so far that lays out the dynamics between all six combined arms elements (or even recognises the seventh) properly. In fact, a written theoretical work on combined arms is often stuck at the level of explaining the three obvious elements and their dynamics.
It appears as if there's a lot of room for improvement in military theory left in regard to combined arms theory.
Too bad; it's overshadowed by small wars with their military intelligence and civ-mil relations emphasis and also overshadowed by the after-effects of RMA (revolution of military affairs; buzzword for a huge confidence in electronic equipment).