Valery A. Liskovets

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We investigate properties of a multivariate function, called orbicyclic, that arises in enumerative combinatorics in counting non-isomorphic maps on orientable surfaces. In particular it is shown that the necessary and sufficient conditions for this function to vanish turn out to be equivalent to familiar Harvey's conditions that characterize finite cyclic(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)
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)