A253948
Number of finite, negative, Archimedean, commutative, totally ordered monoids of size n (semi-groups with a neutral element that is also the top element).
Original entry on oeis.org
1, 1, 1, 2, 6, 22, 95, 471, 2670, 17387, 131753, 1184059, 12896589
Offset: 1
- M. Petrík, GitLab repository with an implementation of the algorithm in Python 3
- M. Petrík, Many-Valued Conjunctions. Habilitation thesis, Czech Technical University in Prague, Faculty of Electrical Engineering, Prague, Czech Republic. Submitted in 2020. Available at Czech Technical University Digital Library.
- M. Petrík and Th. Vetterlein, Rees coextensions of finite tomonoids and free pomonoids. Semigroup Forum 99 (2019) 345-367. DOI: 10.1007/s00233-018-9972-z.
- M. Petrík and Th. Vetterlein, Rees coextensions of finite, negative tomonoids. Journal of Logic and Computation 27 (2017) 337-356. DOI: 10.1093/logcom/exv047.
- M. Petrík and Th. Vetterlein, Algorithm to generate finite negative totally ordered monoids. In: IPMU 2016: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Eindhoven, Netherlands, June 20-24, 2016.
- M. Petrík and Th. Vetterlein, Algorithm to generate the Archimedean, finite, negative tomonoids. In: Joint 7th International Conference on Soft Computing and Intelligent Systems and 15th International Symposium on Advanced Intelligent Systems. Kitakyushu, Japan, Dec. 3-6, 2014. DOI: 10.1109/SCIS-ISIS.2014.7044822.
- Index entries for sequences related to monoids
A253949
Number of finite, negative, Archimedean, totally ordered monoids of size n (semi-groups with a neutral element that is also the top element).
Original entry on oeis.org
1, 1, 1, 2, 8, 44, 333, 3543, 54954, 1297705, 47542371
Offset: 1
- M. Petrík, GitLab repository with an implementation of the algorithm in Python 3
- M. Petrík, Many-Valued Conjunctions. Habilitation thesis, Czech Technical University in Prague, Faculty of Electrical Engineering, Prague, Czech Republic. Submitted in 2020. Available at Czech Technical University Digital Library.
- M. Petrík and Th. Vetterlein, Rees coextensions of finite tomonoids and free pomonoids. Semigroup Forum 99 (2019) 345-367. DOI: 10.1007/s00233-018-9972-z.
- M. Petrík and Th. Vetterlein, Rees coextensions of finite, negative tomonoids. Journal of Logic and Computation 27 (2017) 337-356. DOI: 10.1093/logcom/exv047.
- M. Petrík and Th. Vetterlein, Algorithm to generate finite negative totally ordered monoids. In: IPMU 2016: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Eindhoven, Netherlands, June 20-24, 2016.
- M. Petrík and Th. Vetterlein, Algorithm to generate the Archimedean, finite, negative tomonoids. In: Joint 7th International Conference on Soft Computing and Intelligent Systems and 15th International Symposium on Advanced Intelligent Systems. Kitakyushu, Japan, Dec. 3-6, 2014. DOI: 10.1109/SCIS-ISIS.2014.7044822.
- Index entries for sequences related to monoids
A374293
a(n)/binomial(n,2)! is the probability that the minimum spanning tree of the complete graph of n vertices with i.i.d. random edge weights is a specific path.
Original entry on oeis.org
1, 1, 2, 44, 27120, 882241920, 2443792425984000, 846533597741050576896000, 50571850611494440562578575851520000, 686805008584962439650318114385825747697664000000, 2701735270674169239689693528384644314472371275610193920000000000, 3819958423456547324072333722421751679308286064300212197312630212725309440000000000
Offset: 1
a(3) = 2 because there are 2 orderings of the edges a, b, and c of K_3 that give the path {a, b}: (a, b, c) and (b, a, c).
- Jamie Tucker-Foltz, Table of n, a(n) for n = 1..16
- Eric Babson, Moon Duchin, Annina Iseli, Pietro Poggi-Corradini, Dylan Thurston, and Jamie Tucker-Foltz, Models of Random Spanning Trees, arXiv:2407.20226 [math.CO], 2024.
- Jamie Tucker-Foltz, Code to compute a(n) on GitHub.
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E(p,m)={sum(k=0, m, sum(i=0, k, polcoef(p, i)*i!*(m-i)! )*x^k/(k!*(m-k)!))}
seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, my(p=sum(k=1, n-1, v[k]*v[n-k])); v[n]=E(intformal(p), binomial(n,2))); vector(n, n, my(m=binomial(n,2)); m!*polcoef(v[n], m))} \\ Andrew Howroyd, Jul 31 2024
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