Elena Barcucci

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Reconstructing discrete bidimensional sets from their projections is involved in many different problems of computer-aided tomography, pattern recognition, image processing and data compression. In this paper, we examine the problem of reconstructing a discrete bidimensional set S satisfying some convexity conditions from its two orthogonal projections (H,(More)
In a previous report, we studied the problem of reconKuba’s heuristic algorithm [7] reconstructs some convex sets. structing a discrete set S from its horizontal and vertical projections. Some of the properties imposed on the sets eliminate all ambiguWe defined an algorithm that decides whether there is a convex polyity [4] , while some others only(More)
A permutation is said to be –avoiding if it does not contain any subsequence having all the same pairwise comparisons as . This paper concerns the characterization and enumeration of permutations which avoid a set of subsequences increasing both in number and in length at the same time. Let be the set of subsequences of the form “ ”, being any permutation(More)
The problem of exhaustively generating combinatorial objects can currently be applied to many disciplines, such as biology, chemistry, medicine and computer science. A well known approach to the exhaustive generation problem is given by the Gray code scheme for listing n-bit binary numbers in such a way that successive numbers differ in exactly one bit(More)
In this paper we study the class of generalized Motzkin paths with no hills and prove some of their combinatorial properties in a bijective way; as a particular case we have the Fine numbers, enumerating Dyck paths with no hills. Using the ECO method, we define a recursive construction for Dyck paths such that the number of local expansions performed on(More)
A permutation avoids the subpattern i3 has no subsequence having all the same pairwise comparisons as , and we write ∈ S( ). We examine the classes of permutations, S(321); S(321; 37 142) and S(4231; 4132), enumerated, respectively by the famous Catalan, Motzkin and Schr; oder number sequences. We determine their generating functions according to their(More)
For every integer j¿1, we de ne a class of permutations in terms of certain forbidden subsequences. For j = 1, the corresponding permutations are counted by the Motzkin numbers, and for j =∞ (de ned in the text), they are counted by the Catalan numbers. Each value of j¿ 1 gives rise to a counting sequence that lies between the Motzkin and the Catalan(More)