In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two ...In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.展开更多
In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting e...In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.展开更多
This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit ...This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.展开更多
文摘In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.
文摘In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.
基金NNSFC under Grant No.60373030 and Grant No.10571031
文摘This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.
