منابع مشابه
Permutation Reconstruction
In this paper, we consider the problem of permutation reconstruction. This problem is an analogue of graph reconstruction, a famous question in graph theory. In the case of permutations, the problem can be stated as follows: In all possible ways, delete k entries of the permutation p = p1p2p3...pn and renumber accordingly, creating (n k ) substrings. How large must n be in order for us to be ab...
متن کاملPermutation Reconstruction from Differences
We prove that the problem of reconstructing a permutation π1, . . . , πn of the integers [1 . . . n] given the absolute differences |πi+1 − πi|, i = 1, . . . , n − 1 is NP– complete. As an intermediate step we first prove the NP–completeness of the decision version of a new puzzle game that we call Crazy Frog Puzzle. The permutation reconstruction from differences is one of the simplest combina...
متن کاملPermutation Reconstruction from Minors
We consider the problem of permutation reconstruction, which is a variant of graph reconstruction. Given a permutation p of length n, we delete k of its entries in each possible way to obtain (n k ) subsequences. We renumber the sequences from 1 to n−k preserving the relative size of the elements to form (n−k)-minors. These minors form a multiset Mk(p) with an underlying set M ′ k(p). We study ...
متن کاملPermutation Reconstruction from MinMax-Betweenness Constraints
In this paper, we investigate the reconstruction of permutations on {1, 2, . . . , n} from betweenness constraints involving the minimum and the maximum element located between t and t + 1, for all t = 1, 2, . . . , n − 1. We propose two variants of the problem (directed and undirected), and focus first on the directed version, for which we draw up general features and design a polynomial algor...
متن کاملPermutation-equivariant Quantum K-theory Viii. Explicit Reconstruction
In Part VII, we proved that the range LX of the big J-function in permutation-equivariant genus-0 quantum K-theory is an overruled cone, and gave its adelic characterization. Here we show that the ruling spaces are Dq-modules in Novikov’s variables, and moreover, that the whole cone LX is invariant under a large group of symmetries of LX defined in terms of q-difference operators. We employ thi...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1149