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A Combinatorial Question Related to an Easter Tradition Led to a New Entry in OEIS

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Ivaylo Kortezov
Bulgarian Academy of Sciences

https://doi.org/10.53656/math2021-2-8-aco

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.
Keywords: combinatorics; swap; inversion; invariant; paths in a lattice

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    • Pedagogika-Pedagogy
    • Mathematics and Informatics
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    • Vocational Education
    • Istoriya-History journal
    • Chuzhdoezikovo Obuchenie-Foreign Language Teaching
    • Filosofiya-Philosophy
  • Monographs, Proceedings
    • Demographic Situation and Labour Market in Blagoevgrad and Kyustendil Districts
    • Proceeding of 1st International Conference on Environmental Protection and Disaster RISKs
    • Bulgaria - North Macedonia - Slovenia: Intercultural Dialogues in XXI Century
    • Europe’s Core-Periphery Relations and Horizontal Disparities
    • Bulgaria - Macedonia - Slovenia: Intercultural Dialogues in the 21st Century, Part II
    • Local and Regional Aspects of Natural Hazards
    • ADAPTED METHODOLOGY OF HISTORY EDUCATION
    • VASIL LEVSKI. FROM THE CURVES OF LITERARY ICONOGRAPHY
    • Bulgaria - Macedonia - Slovenia: Intercultural Dialogues in the 21st Century
    • Gender World In Different Cultural Models
    • ADAPTED METHODOLOGY OF HISTORY EDUCATION 2
    • THEORETICAL MODEL FOR A CUMULATIVE LEXICOGRAPHING OF WORDS OF FOREIGN ORIGIN IN THE BULGARIAN LANGUAGE
    • БЪЛГАРСКИЯТ ЕЗИК, ЛИТЕРАТУРА И КУЛТУРА: ПЪТИЩА ПРЕЗ МУЛТИКУЛТУРНИЯ СВЯТ
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