A321309 -id:A321309 - cp's OEIS frontend

A373089 Coefficients of the power series expansion at p=1 of the time constant C(-1,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -1 with respective probabilities p and 1-p.

1, 1, 1, 3, 7, 15, 30, 60, 123, 254, 517, 1040, 2093, 4226, 8523, 17146, 34469, 69295, 139263, 279803, 562076, 1128834, 2266768, 4551848, 9139963, 18350850, 36842933, 73969425, 148503840, 298134233, 598527760, 1201583460, 2412228147, 4842626698, 9721723262, 19516574603

Offset: 0

Benjamin Terlat, May 23 2024

nonn

C(-1,p) is also the speed of the front for an interacting particle system with 2 bins, which corresponds to the particular case of the max-growth system where the probability distribution has two atoms 1 and -1 with respective probabilities p and 1-p.

The first 6 coefficients of this sequence coincide with the first 6 coefficients of A321309.

			C(-1,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...

Benjamin Terlat, Table of n, a(n) for n = 0..1000
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models, arXiv:2312.02884 [math.PR], 2023.
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation, arXiv:2110.01559 [math.PR], 2023.

Cf. A321309, A373090, A373091.

A373090 Coefficients of the power series expansion at p=1 of the time constant C(-2,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -2 with respective probabilities p and 1-p.

Original entry on oeis.org

1, 1, 1, 3, 7, 15, 29, 54, 102, 197, 376, 695, 1260, 2286, 4155, 7489, 13347, 23621, 41609, 72884, 126789, 218903, 375140, 638554, 1079382, 1809256, 3003411, 4934260, 8013764, 12839395, 20232603, 31228335, 46918878, 67947178, 93185004, 116654299, 120921410, 63471736, -150813354, -723950195

Offset: 0

Benjamin Terlat, May 23 2024

sign

C(-2,p) is also the speed of the front for an interacting particle system with 3 bins, which corresponds to the particular case of the max-growth system where the probability distribution has two atoms 1 and -2 with respective probabilities p and 1-p.

The first 10 coefficients of this sequence coincide with the first 10 coefficients of A321309.

			C(-2,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...

Benjamin Terlat, Table of n, a(n) for n = 0..1250
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models, arXiv:2312.02884 [math.PR], 2023.
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation, arXiv:2110.01559 [math.PR], 2023.

Cf. A321309, A373089, A373091.

A373091 Coefficients of the power series expansion at p=1 of the time constant C(-3,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -3 with respective probabilities p and 1-p.

Original entry on oeis.org

1, 1, 1, 3, 7, 15, 29, 54, 102, 197, 375, 687, 1226, 2182, 3885, 6827, 11757, 19920, 33339, 55012, 88980, 140141, 213535, 311997, 428578, 527659, 506451, 118728, -1180673, -4546846, -12344870, -29279209, -64481947, -135339292, -274463246, -542210697, -1048748528, -1992459450

Offset: 0

Benjamin Terlat, May 23 2024

sign

C(-3,p) is also the speed of the front for an interacting particle system with 4 bins, which corresponds to the particular case of the max-growth system where the probability distribution has two atoms 1 and -3 with respective probabilities p and 1-p.

The first 15 coefficients of this sequence coincide with the first 15 coefficients of A321309.

			C(-3,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...

Benjamin Terlat, Table of n, a(n) for n = 0..750
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models, arXiv:2312.02884 [math.PR], 2023.
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation, arXiv:2110.01559 [math.PR], 2023.

Cf. A321309, A373089, A373090.

cp's OEIS Frontend

A373089 Coefficients of the power series expansion at p=1 of the time constant C(-1,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -1 with respective probabilities p and 1-p.

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A373090 Coefficients of the power series expansion at p=1 of the time constant C(-2,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -2 with respective probabilities p and 1-p.

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A373091 Coefficients of the power series expansion at p=1 of the time constant C(-3,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -3 with respective probabilities p and 1-p.

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Author

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