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COUNING g-ESSENTIAL MAPS ON SURFACES WITH SMALL GENERA
Rongxia Hao,Junliang Cai,Yanpei Liu 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
This paper provides some functional equations and parametric expressions of {\t$g$}-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further. This paper provides some functional equations and parametric expressions of {\t$g$}-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.
COUNING g-ESSENTIAL MAPS ON SURFACES WITH SMALL GENERA
Hao, Rongxia,Cai, Junliang,Liu, Yanpel 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.
THE ENUMERATION OF ROOTED CUBIC C-NETS
CAI, JUNLIANG,HAO, RONGXIA,LID, YANPEI 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].
The enumeration of rooted cubic c-nets$^{\dag}$
Junliang Cai,Rongxia Hao,Yanpei Liu 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].