We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple...

We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple...

Abstract. We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular holes in a “sea” of dimers. We determine the asymptotics of the joint correlation (for large separations between the holes) in the case when one of the holes has side 1, all remainin...

We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple...

We study systematically the ≃ 0.1 − 1200 Hz quasi-periodic oscillations (QPOs) and broad noise components observed in the power spectra of non-pulsing neutron-star and black-hole low-mass X-ray binaries. We show that among these components we can identify two, occurring over a wide range of source types and luminosities, whose frequencies follow a tight correlation. The variability components i...