Valery A. Liskovets

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Sum-free enumerative formulae are derived for several classes of rooted planar maps with no vertices of odd valency (eulerian maps) and with two vertices of odd valency (unicursal maps). As corollaries we obtain simple formulae for the numbers of unrooted eulerian and unicursal planar maps. Also, we obtain a sum-free formula for the number of rooted(More)
We present a formula for the number of n-edge unrooted loopless planar maps considered up to orientation-preserving isomorphism. The only sum contained in this formula is over the divisors of n. Résumé. Nous présentons une formule pour le nombre de cartes planaires sans boucles avec n arêtes, ` a isomorphisme près préservant l'orientation. La seule somme(More)
We propose and discuss several simple ways of obtaining new enumerative sequences from existing ones. For instance, the number of graphs considered up to the action of an involutory transformation is expressible as the semi-sum of the total number of such graphs and the number of graphs invariant under the involution. Another, less familiar idea concerns(More)