On the enumeration of some inequivalent monotone Boolean functions

References

• Sloane NJA. The online encyclopedia of integer sequences. 1964. Available from: https://oeis.org/.
   Google Scholar
• Church R. Numerical analysis of certain free distributive structures. Duke Math J. 1940;6(3):732–734.
   Google Scholar
• Ward M. Note on the order of free distributive lattices. Bull New Ser Am Math Soc. 1946;52:423.
   Web of Science ®Google Scholar
• Church R. Enumeration by rank of the free distributive lattice with 7 generators. Not Am Math Soc. 1965;11:724.
   Google Scholar
• Berman J, Khler P. Cardinalities of finite distributive lattices. Mitt Math Sem Giessen. 1976;121:103–124.
   Google Scholar
• Wiedemann D. A computation of the eighth Dedekind number. Order. 1991;8(1):5–6.
   Google Scholar
• Fidytek R, Mostowski A, Somla R, et al. Algorithms counting monotone Boolean functions. Inf Process Lett. 2001;79:203–209.
   Web of Science ®Google Scholar
• Stephen T, Yusun T. Counting inequivalent monotone Boolean functions. Discrete Appl Math. 2014;167:15–24.
   Web of Science ®Google Scholar
• Pawelski B. On the number of inequivalent monotone Boolean functions of 8 variables. 2021. arXiv:2108.13997 [math.CO].
   Google Scholar
• Kurz S, Samaniego D. A note on simple games with two equivalence classes of players. 2021. arXiv:2112.00307.
   Google Scholar
• Alonso-Meijide JM, Bilbao JM, Casas-Méndez B, et al. Weighted multiple majority games with unions: generating functions and applications to the European union. Eur J Oper Res. 2009;198:530–544.
   Web of Science ®Google Scholar
• Felsenthal DS, Machover M. The measurement of voting power. Cheltenham: Edward Elgar Publishing Limited; 1998.
   Google Scholar
• Freixas J. The dimension for the European union council under the nice rules. Eur J Oper Res. 2004;156(2):415–419.
   Web of Science ®Google Scholar
• Kilgour DM. A formal analysis of the amending formula of Canada's constitution act. Can J Polit Sci. 1983;16:771–777.
   Web of Science ®Google Scholar
• Le Breton M, Montero M, Zaporozhets V. Voting power in the EU council of ministers and fair decision making in distributive politics. Math Soc Sci. 2012;63:159–173.
   Web of Science ®Google Scholar
• Leech D. Voting power in the governance of the international monetary fund. Ann Oper Res. 2002;109:375–397.
   Web of Science ®Google Scholar
• Taylor AD, Pacelli A. Mathematics and politics. 2nd ed. New York: Springer Verlag; 2008.
   Google Scholar
• Isbell JR. A class of majority games. Q J Math. 1956;7(2):183–187.
   Google Scholar
• Maschler M, Peleg B. A characterization, existence proof, and dimension bounds for the kernel of a game. Pacific J Math. 1966;18:289–328.
   Web of Science ®Google Scholar
• Álvarez-Mozos M, Ferreira F, Alonso-Meijide JM, et al. Characterizations of power indices based on null free winning coalitions. Optimization. 2015;64(3):675–686.
   Web of Science ®Google Scholar
• Einy E. The desirability relation of simple games. Math Soc Sci. 1985;10(2):155–168.
   Web of Science ®Google Scholar
• Freixas J. On ordinal equivalence of the Shapley and Banzhaf values for cooperative games. Int J Game Theory. 2010;39:513–527.
   Web of Science ®Google Scholar
• Freixas J, Marciniak D, Pons M. On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices. Eur J Oper Res. 2012;216:367–375.
   Web of Science ®Google Scholar
• Freixas J, Pons M. Hierarchies achievable in simple games. Theory Decis. 2010;68(4):393–404.
   Web of Science ®Google Scholar
• Friedman J, McGrath L, Parker C. Achievable hierarchies in voting games. Theory Decis. 2006;61(4):305–318.
   Web of Science ®Google Scholar
• Kurz S. On the inverse power index problem. Optimization. 2012;61(8):989–1011.
   Web of Science ®Google Scholar
• Lambo LD, Moulen J. Ordinal equivalence of power notions in voting games. Theory Decis. 2002;53:313–325.
   Web of Science ®Google Scholar
• Axenovich M, Roy S. On the structure of minimal winning coalitions in simple voting games. Soc Choice Welfare. 2010;34(3):429–440.
   Web of Science ®Google Scholar
• Carreras F, Freixas J. Complete simple games. Math Soc Sci. 1996;32(2):139–155.
   Web of Science ®Google Scholar
• Einy E, Lehrer E. Regular simple games. Int J Game Theory. 1989;18(2):195–207.
   Web of Science ®Google Scholar
• Kurz S, Tautenhahn N. On Dedekind's problem for complete simple games. Int J Game Theory. 2013;42(2):411–437.
   Web of Science ®Google Scholar
• Taylor AD, Zwicker WS. Simple games: desirability relations, trading, and pseudoweightings. Princeton (NJ): Princeton University Press; 1999.
   Google Scholar
• Freixas J, Samaniego D. On the enumeration of bipartite simple games. Discret Appl Math. 2021;297:129–141.
   Web of Science ®Google Scholar
• Felsenthal DS, Machover M, Zwicker WS. The bicameral postulates and indices of a priori voting power. Theory Decis. 1998;44(1):83–116.
   Web of Science ®Google Scholar
• Freixas J, Kurz S. Enumerations of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum. Ann Oper Res. 2014;222:317–339.
   Web of Science ®Google Scholar
• Freixas J, Molinero X, Roura S. Complete voting systems with two types of voters: weightedness and counting. Ann Oper Res. 2012;193(1):273–289.
   Web of Science ®Google Scholar
• Herranz J. Any 2-asummable bipartite function is weighted threshold. Discret Appl Math. 2011;159:1079–1084.
   Web of Science ®Google Scholar
• Freixas J, Kurz S. The golden number and Fibonacci sequences in the design of voting systems. Eur J Oper Res. 2013;226(2):246–257.
   Web of Science ®Google Scholar
• Peleg B. Coalition formation in simple games with dominant players. Int J Game Theory. 1981;10:11–33.
   Google Scholar
• Freixas J. On the enumeration of Boolean functions with distinguished variables. Soft Comput. 2021;25:12627–12640.
   Web of Science ®Google Scholar
• Freixas J, Freixas M, Kurz S. On the characterization of weighted simple games. Theory Decis. 2017;83(4):469–498.
   Web of Science ®Google Scholar
• Freixas J, Molinero X. Simple games and weighted games: a theoretical and computational viewpoint. Discret Appl Math. 2009;157(7):1496–1508.
   Web of Science ®Google Scholar
• Herranz J, Sáez G. New results on multipartite access structures. IEE Proc Inf Secur. 2006;153(4):153–162.
   Google Scholar
• Taylor AD, Zwicker WS. Weighted voting, multicameral representation, and power. Games Econ Behav. 1993;5:170–181.
   Web of Science ®Google Scholar