The Ceriani-Frolkin theme (named after two giant retro-masters) is a famous theme in retro-problems. It can be defined as a promotion followed by the capture of the promotee.
The paradoxical aspect of this theme is that simple balance arguments cannot tell us the nature of the promoted unit. Once the promotee is captured, not much footsteps or scars are left to observe.
Here is a schema exemplifying why:
Here Bl. is missing one Rook. Wh. is missing his Queen and his h2 Pawn. Bl. captured via b7xa6 and h7xg6. The position of the Nh8 requires that it reached h8 before h7xg6 took place, so that the missing bl. R has been captured on g8 or h8 and the wPh2 could not reach the g-file via e.g. h4xRg5.
The only way the wPh2 could get captured on g6 (or a6) is after a
promotion. What must have happened is:
1. bKR goes to g8, bN to h8,
2. then wQ gets captured on g6, entombing the Nh8,
3. then wPh2 reaches h7, captures and promotes with Ph7xRg8.
The tangled NE corner forbids a promotion into B or R. Still we cannot say whether it was into Q or N ! Also we would like to say that the promoted unit has been captured on a6. But this needs not be so. Indeed, the promoted unit can very well be one of the wh. Knights present in the diagram.
Clearly, more complex constructions are required to display a correct Ceriani-Frolkin promotion !!
Europe Echecs 385, 01/1991
4th-5th Comm. Europe Echecs 91-92
11+13. History of the wh. Pawns?
Bl. caps are h7xg6, cxdxe & exfxg. To fit the balance, wPa2, b2, and c2 had to promote (on b8 and c8) after a6xb7 and bxc. Third wh. cap. is fxe so that wPg2 got captured on its file and wPh2 promoted on h8.
Position unlocks by retracting: -1. d6xNe5+ Nc6-e5+ -2. f4xNg3 Nb8-c6 -3. f5-f4 b7-b8=N -4. e6xNf5 a6xRb7 and bl. retropat is avoided.
Unlocking goes on with unpromoting uncaptured wNg3 and wNf5 on c8. Then c7xQd6 can be retracted and the Qd6 unpromoted on h8. Then h7xPg6 unlocks everything.
Quadruple Ceriani-Frolkin theme with Q+3N.
Many problems of the Shortest Proof Game genre display Ceriani-Frolkin promotions. Here time-pressure and the necessity of not checking the enemy King are often used to enforce promotion into a specific unit.
Here is a very economical example:
Europe Echecs 316, 04/1985
2nd Prize Europe Echecs 85-86
14+11. Position after Wh. 27th move. Game score?
1. f4 h5 2. f5 h4 3. f6 h3 4. fxe7 hxg2 5. h4 g5 6. h5 g4 7. Rh4 g3 8. Nh3 g1=B 9. Bg2 Be3 10. Bc6 g2 11. dxe3 g1=R 12. Kf2 Rg3 13. e4 Rb3 14. axb3 f5 15. Ra6 f4 16. Ba4 f3 17. Kg3 f2 18. Rh6 f1=Q 19. Qd6 Qf7 20. Bf4 Qc4 21. bxc4 a5 22. Bb3 a4 23. Qa6 a3 24. Bd6 a2 25. Nf4 axb1=N 26. Ba2 Nc3 27. bxc3
All four Frolkin promotions in a very economical SPG.