We enumerate rooted triangulations of a sphere with multiple holes by the total number of edges and the length of each boundary component. The proof relies on a combinatorial identity due to W.T. Tutte.

Recently, Green and Losonczy [5, 6] introduced freely braided permutations as a special class of restricted permutations that has arisen in the study of Schubert varieties. They suggest as an open problem to enumerate the number of freely braided permutations in Sn. In this paper, we prove that the generating function for the number of freely braided permutations in Sn is given by 1−3x−2x2 +(1+...

We show that if A and B form a nontrivial K-pair, then there is a semi-computable set C such that A ≤e C and B ≤e C. As a consequence, we obtain a definition of the total enumeration degrees: a nonzero enumeration degree is total if and only if it is the join of a nontrivial maximal K-pair. This answers a long-standing question of Hartley Rogers, Jr. We also obtain a definition of the “c.e. in”...

We prove that no subclass of the Σ 2 enumeration degrees containing the 3-c.e. enumeration degrees can be cupped to 0e by a single Σ 2 enumeration degree.

We contribute to the study of efficient enumeration algorithms for all solutions of constraint satisfaction problems. The only algorithm known so far, presented by Creignou and Hébrard [CH97] and generalized by Cohen [Coh04], reduces the enumeration problem for a constraint language Γ to the decision problem for a slightly enlarged constraint language Γ, i.e., it yields an efficient enumeration...