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- W1842804924 abstract "We present uniformly available simple enumerative formulae for unrooted planar $n$-edge maps (counted up to orientation-preserving isomorphism) of numerous classes including arbitrary, loopless, non-separable, eulerian maps and plane trees. All the formulae conform to a certain pattern with respect to the terms of the sum over $tmid n,,t! < !n.$ Namely, these terms, which correspond to non-trivial automorphisms of the maps, prove to be of the form $phileft({nover t}right)alpha,r^t {k,tchoose t}$, where $phi(m)$ is the Euler function, $k$ and $r$ are integer constants and $alpha$ is a constant or takes only two rational values. On the contrary, the main, rooted summand corresponding to $t=n$ contains an additional factor which is a rational function of $n$. Two simple new enumerative results are deduced for bicolored eulerian maps. A collateral aim is to briefly survey recent and old results of unrooted planar map enumeration." @default.
- W1842804924 created "2016-06-24" @default.
- W1842804924 creator A5073772029 @default.
- W1842804924 date "2004-12-07" @default.
- W1842804924 modified "2023-10-18" @default.
- W1842804924 title "Enumerative Formulae for Unrooted Planar Maps: a Pattern" @default.
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- W1842804924 doi "https://doi.org/10.37236/1841" @default.
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