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THE HOPF MONOID AND THE BASIC INVARIANT OF DIRECTED GRAPHS

Kato, Keiju 大阪大学 DOI:10.18910/83201

2021.07

概要

Aguiar and Ardila defined the Hopf monoid GP of generalized permutahedra and showed that it contains many submonoids that correspond to combinatorial objects. They also give a basic polynomial invariant of generalized permutahedra, which then specializes to submonoids. We define the Hopf monoid of directed graphs and show that it also embeds in GP. The resulting basic invariant coincides with the strict chromatic polynomial of Awan and Bernardi.

参考文献

[1] M. Aguiar and F. Ardila: Hopf monoids and generalized permutahedra, arXiv:1709.07504.

[2] M. Aguiar and S. Mahajan: Monoidal functors, species and Hopf algebras, American Mathematical Society, Providence, R.I., New York, 2010.

[3] J. Awan and O. Bernardi: Tutte polynomials for directed graphs, J. Combin. Theory, Seri. B 140 (2019), 192–247.

[4] M. Beck and S. Robins: Computing the Continuous Discretely, Springer, New York, 2015.

[5] F. Bergeron, G. Labelle, and P. Leroux: Combinatorial species and tree-like structures, Cambridge University Press, Cambridge, 1998.

[6] L.J. Billera, N. Jia, and V. Reiner: A quasisymmetric function for matroids, European J. Combin. 30 (2009), 1727–1757.

[7] J. Edmonds: Submodular functions, matroids, and certain polyhedral; in Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969), Gordon and Breach, New York, 1970, 69–87.

[8] S. Fujishige: Submodular functions and optimization, second edition, Annals of Discrete Mathematics 58, Elsevier B. V., Amsterdam, 2005.

[9] S.A. Joni and G.C. Rota: Coalgebras and bialgebras in combinatorics; in Umbral Calculus and Hopf Algebras (Norman, OKla, 1978), Contemporary Mathematics 6, Amer. Math. Soci., Providence, R.I., 1982, 1–47.

[10] A. Joyal: Une th´eorie combinatoire des s´eries formelles, Adva. Math. 42 (1981), 1–82.

[11] A. Postnikov: Permutohedra, Associahedra, and Beyond, Int. Math. Re. Not. IMRN (2009), 1026–1106.

[12] W.R. Schmitt: Hopf algebras of combinatorial structures, Canad. J. Math. 45 (1993), 412–428.

[13] A. Schrijver: Combinatorial optimization: polyhedra and efficiency, Springer-Verlag, Berlin Heidelberg,2003.

[14] P.R. Stanley: Ordered structures and partitions, Memoirs of American Mathematical Society, no. 119, American Mathematical Society, Providence, New York, 1972.

[15] P.R. Stanley: Acyclic orientations of graphs, Discrete Math. 5 (1973), 171–178.

[16] R.P. Stanley: Combinatorics and commutative algebra, Progress in Mathematics 41, Springer, New York, 2007.

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