What is it about?
An inversion sequence is a certain coding for a permutation. For example 123 has inversion sequence 000, and 321 has inversion sequence 012. Parameters in the inversion sequence contain certain information such as the degree of order of the permutation. In this paper we study various parameters in the inversion sequence in their own right.
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Why is it important?
Inversion sequences are currently much researched objects. Mainly other research has focused on the detection or avoidance of mathematical patterns in inversion sequences. Our focus is not on patterns but rather on the relationship of parts of the inversion sequence with other parts and by using bijections whether a particular detected relationship, say between two given parts corresponds to some other relationship between perhaps two different parts. In other words we are researching the relationship between parts of the inversion sequence.
Perspectives
I believe this is important because permutations are ubiquitous and long standing in mathematics and the study of inversion sequences adds new perspectives in the study of permutations that were not apparent, understood or researched previously. For example, a measure of the degree of disorder in a permutation may be researched using inversion sequences.
Aubrey Blecher
University of the Witwatersrand
Read the Original
This page is a summary of: Parameters in Inversion Sequences, Mathematica Slovaca, June 2023, De Gruyter,
DOI: 10.1515/ms-2023-0041.
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