A289684
Mixing moments for the waiting time in an M/G/1 waiting queue.
Original entry on oeis.org
1, 2, 9, 42, 199, 950, 4554, 21884, 105323, 507398, 2446022, 11796884, 56912838, 274630876, 1325431956, 6397576888, 30882340531, 149084312006, 719736965358, 3474807470756, 16776410481266, 80998307687668, 391074406408716, 1888199373821896, 9116752061308798
Offset: 0
- Robert Israel, Table of n, a(n) for n = 0..1461
- J. Abate and W. Whitt, Integer Sequences from Queueing Theory, J. Int. Seq. 13 (2010), 10.5.5, eq. (30) and (32).
- Alexander Karpov, Klas Markström, Søren Riis and Bei Zhou, Bipartite peak-pit domains, arXiv:2308.02817 [cs.DM], 2023-2024.
- Alexander Karpov, Klas Markström, Søren Riis, and Bei Zhou, Coherent domains and improved lower bounds for the maximum size of Condorcet domains, Discrete Applied Mathematics, Volume 370, Pages 57-70 (2025). See pp. 68-69.
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f:= gfun:-rectoproc({n*a(n) +2*(-4*n+3)*a(n-1) +12*(n-2)*a(n-2) +8*(2*n-3)*a(n-3),a(0)=1,a(1)=2,a(2)=9,a(3)=42},a(n),remember):
map(f, [$0..50]); # Robert Israel, Mar 31 2019
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CoefficientList[2 x^2/(4 x^2 + 2x + Sqrt[1 - 4x] - 1) + O[x]^25, x] (* Jean-François Alcover, Aug 26 2022 *)
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(2*x^2/(4*x^2+2*x+sqrt(1-4*x)-1)).series(x, 25).coefficients(x, sparse=False) # Stefano Spezia, Mar 19 2025
A369614
Maximal size of Condorcet domain on n alternatives.
Original entry on oeis.org
1, 1, 2, 4, 9, 20, 45, 100, 224
Offset: 0
For n <= 2, the set of all n! permutations is a Condorcet domain.
For n = 3, an example of a Condorcet domain of maximal size is the following set of permutations:
123
213
231
321
For n = 4, an example of a Condorcet domain of maximal size is:
1234
1324
1342
3124
3142
3412
3421
4312
4321
- Dolica Akello-Egwell, Charles Leedham-Green, Alastair Litterick, Klas Markström and Søren Riis, Condorcet Domains of Degree at most Seven, arXiv:2306.15993 [cs.DM], 2023. See the website presenting all maximal unitary Condorcet domains on 4, 5, 6, 7 alternatives.
- Clemens Puppe and Arkadii Slinko, Maximal Condorcet domains: A further progress report, KIT Working Paper Series in Economics, 159 (2022).
- Charles Leedham-Green, Klas Markström and Søren Riis, The largest Condorcet domain on 8 alternatives, Soc. Choice Welf., 62 (2024), 109-116.
- Bernard Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160; preprint: halshs-00198635.
- Wikipedia, Condorcet paradox.
Cf.
A144685 (size of Fishburn's alternating domain),
A144686 (maximal size of Condorcet domain containing a maximal chain),
A144687,
A289684.
A144686
Maximal size of a connected acyclic domain of permutations of n elements with diameter n*(n-1)/2.
Original entry on oeis.org
1, 2, 4, 9, 20, 45, 100
Offset: 1
- B. Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160.
- James Abello, The Weak Bruhat Order of S_Sigma, Consistent Sets, and Catalan Numbers, SIAM Journal on Discrete Mathematics, 4 (1991), 1-16; alternative link.
- James Abello, The Majority Rule and Combinatorial Geometry (via the Symmetric Group), Annales Du Lamsade, 3 (2004), 1-13.
- Vladimir I. Danilov, Alexander V. Karzanov, and Gleb Koshevoy, Condorcet domains of tiling type, Discrete Applied Mathematics 160.7-8 (2012), pages 933-940.
- Stefan Felsner and Pavel Valtr, Coding and counting arrangements of pseudolines, Discrete & Computational Geometry 46.3 (2011), pages 405-416.
- Alexander Karpov and Arkadii Slinko, Constructing large peak-pit Condorcet domains, Theory and Decision, 94 (2023), 97-120.
- B. Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160 ⟨halshs-00198635⟩.
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