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math.CO2023
Structural and Combinatorial Properties of 2-swap Word Permutation Graphs
Duncan Adamson, Nathan Flaherty, Igor Potapov +1
In this paper, we study the graph induced by the permutation on words with a fixed Parikh vector. A -swap is defined as a pair of positions where…
math.CO2021
Combinatorial Algorithms for Multidimensional Necklaces
Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev +1
A necklace is an equivalence class of words of length over an alphabet under the cyclic shift (rotation) operation. As a classical object, there have been many algorithmic resu…
math.CO2021
Ranking Bracelets in Polynomial Time
Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev +1
The main result of the paper is the first polynomial-time algorithm for ranking bracelets. The time-complexity of the algorithm is O(k^2 n^4), where k is the size of the alphabet a…