Some Enumeration Problems in the Duplication-Loss Model of Genome Rearrangement

02/01/2019

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by   Mladen Kovačević, et al.

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Tandem-duplication-random-loss (TDRL) is an important genome rearrangement operation studied in evolutionary biology. This paper investigates some of the formal properties of TDRL operations on the symmetric group (the space of permutations over an n -set). In particular, motivated by error correction and reconstruction problems in DNA-based data storage applications, we determine the size of "balls" of radius one in the TDRL metric, as well as the cardinality of the maximum intersection of two balls. The corresponding problems for the so-called mirror (or palindromic) TDRL rearrangement operations are also investigated.