Smallest posets with given cyclic automorphism group
Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1307-1318.

For each n1 we determine the minimum number of points in a poset with cyclic automorphism group of order n.

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DOI: 10.5802/alco.372
Classification: 06A11, 20B25, 06A07, 05E18
Keywords: Posets, Automorphism group.

Barmak, Jonathan Ariel 1; Barreto, Agustín Nicolás 1

1 Universidad de Buenos Aires Facultad de Ciencias Exactas y Naturales Departamento de Matemática and CONICET-Universidad de Buenos Aires Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS) Buenos Aires Argentina
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Barmak, Jonathan Ariel; Barreto, Agustín Nicolás. Smallest posets with given cyclic automorphism group. Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1307-1318. doi : 10.5802/alco.372. https://alco.centre-mersenne.org/articles/10.5802/alco.372/

[1] Arlinghaus, W.C. The structure of minimal graphs with given abelian automorphism group, Ph. D. Thesis, Wayne State University (1979) https://www.proquest.com/openview/52ea9d895ef8d4684f4980de9375092a

[2] Arlinghaus, W.C. The classification of minimal graphs with given abelian automorphism group, Mem. Amer. Math. Soc., Volume 57 (1985) no. 330, p. viii+86 | DOI | MR | Zbl

[3] Babai, L. On the minimum order of graphs with given group, Canad. Math. Bull., Volume 17 (1974) no. 4, pp. 467-470 | DOI | MR

[4] Babai, L. Finite digraphs with given regular automorphism groups, Period. Math. Hungar., Volume 11 (1980) no. 4, pp. 257-270 | DOI | MR | Zbl

[5] Barreto, A.N. Sobre los posets más chicos con grupo de automorfismos abeliano dado, Tesis de licenciatura, Universidad de Buenos Aires (2021) https://web.dm.uba.ar/files/tesis_lic/2021/barreto.pdf

[6] Birkhoff, G. On groups of automorphisms, Rev. Un. Mat. Argentina, Volume 11 (1946), pp. 155-157 | MR

[7] Frucht, R. Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math., Volume 6 (1939), pp. 239-250 | Numdam | MR | Zbl

[8] Frucht, R. Graphs of degree three with a given abstract group, Canad. J. Math., Volume 1 (1949), pp. 365-378 | DOI | MR | Zbl

[9] Frucht, R. On the construction of partially ordered systems with a given group of automorphisms, Amer. J. Math., Volume 72 (1950), pp. 195-199 | DOI | MR | Zbl

[10] Meriwether, R.L. Smallest graphs with a given cyclic group (see G. Sabidussi, 1967. Math. Rev. 33, 2563) | MR

[11] Sabidussi, G. On the minimum order of graphs with given automorphism group, Monatsh. Math., Volume 63 (1959), pp. 124-127 | DOI | MR | Zbl

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