Generalizations of Khovanskiĭ's theorems on the growth of sumsets in Abelian semigroups

Advances in Applied Mathematics - Tập 41 - Trang 115-132 - 2008
Vít Jelínek1, Martin Klazar1,2
1Department of Applied Mathematics, Faculty of Mathematics and Physics of Charles University, Malostranské náměstí 25, 118 00 Praha, Czech Republic
2Institute for Theoretical Computer Science, Faculty of Mathematics and Physics of Charles University, Malostranské náměstí 25, 118 00 Praha, Czech Republic

Tài liệu tham khảo

Albert Balogh, 2006, Hereditary properties of ordered graphs, 179 Beck, 1999, A closer look at lattice points in rational simplices, Electron. J. Combin., 6, 10.37236/1469 Beck, 2002, Multidimensional Ehrhart reciprocity, J. Combin. Theory Ser. A, 97, 187, 10.1006/jcta.2001.3220 Beck, 2007, Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra W. Bruns, J. Gubeladze, Polytopes, rings and K-theory, preprint, www.mathematik.uni-osnabrueck.de/staff/phpages/brunsw/kripo.pdf Ehrhart, 1962, Sur les polyèdres rationnels homothétiques à n dimensions, C. R. Acad. Sci. Paris, 254, 616 Huczynska, 2006, Grid classes and the Fibonacci dichotomy for restricted permutations, Electron. J. Combin., 13, 10.37236/1080 V. Jelínek, M. Klazar, Polynomial and quasipolynomial counting, in preparation Kaiser, 2003, On growth rates of closed permutation classes, Electron. J. Combin., 9, 10.37236/1682 Khovanskiĭ, 1992, Newton polyhedron, Hilbert polynomial, and sums of finite sets, Funct. Anal. Appl., 26, 276, 10.1007/BF01075048 Khovanskiĭ, 1995, Sums of finite sets, orbits of commutative semigroups, and Hilbert functions, Funct. Anal. Appl., 29, 102, 10.1007/BF01080008 Kruskal, 1972, The theory of well-quasi-ordering: A frequently discovered concept, J. Combin. Theory Ser. A, 13, 297, 10.1016/0097-3165(72)90063-5 Lisoněk, 2007, Combinatorial families enumerated by quasi-polynomials, J. Combin. Theory Ser. A, 114, 619, 10.1016/j.jcta.2006.06.013 Macdonald, 1963, The volume of a lattice polyhedron, Proc. Cambridge Philos. Soc., 59, 719, 10.1017/S0305004100003716 Macdonald, 1971, Polynomials associated with finite cell complexes, J. London Math. Soc. (2), 4, 181, 10.1112/jlms/s2-4.1.181 Matoušek, 2002 Nathanson, 2000, Growth of sumsets in abelian semigroups, Semigroup Forum, 61, 149, 10.1007/PL00006010 Nathanson, 2002, Polynomial growth of sumsets in abelian semigroups, J. Théor. Nombres Bordeaux, 14, 553, 10.5802/jtnb.374 Pouzet Stanley, 1975, Problem E2546, Amer. Math. Monthly, 82, 756, 10.2307/2318742 Stanley, 2002