A Combinatorial Question Related to an Easter Tradition Led to a New Entry in OEIS
A Combinatorial Question Related to an Easter Tradition Led to a New Entry in OEIS
Author(s): Ivaylo KortezovSubject(s): Social Sciences, Education, School education, Vocational Education, Adult Education, Higher Education , State/Government and Education, Inclusive Education / Inclusion, Sociology of Education
Published by: Национално издателство за образование и наука „Аз-буки“
Keywords: combinatorics; swap; inversion; invariant; paths in a lattice
Summary/Abstract: In some regions of Bulgaria (at least) there is an Easter tradition, according to which in group of people first each one chooses a differently coloured egg, then each pair of people performs a swap (or swaps) by exchanging the eggs they currently have until everyone gets the originally chosen egg. This generates a natural question: if there are n people in the group, find the least number E(n) of swaps which makes this possible. We prove that E(n) is the least even number not less than n(n−1)/2. The sequence thus generated was added to the Online Encyclopedia of Integer Sequences and linked from there to several seemingly distant combinatorial results.
Journal: Математика и информатика
- Issue Year: 64/2021
- Issue No: 2
- Page Range: 222-225
- Page Count: 4
- Language: English
- Content File-PDF