{"id":241,"date":"2026-01-29T03:19:17","date_gmt":"2026-01-29T03:19:17","guid":{"rendered":"https:\/\/mrc-baku.org\/?p=241"},"modified":"2026-05-01T03:27:39","modified_gmt":"2026-05-01T03:27:39","slug":"general-seminar-by-erkko-lehtonen-khalifa-university-uae","status":"publish","type":"post","link":"https:\/\/mrc-baku.org\/index.php\/general-seminar-by-erkko-lehtonen-khalifa-university-uae\/","title":{"rendered":"General Seminar by Erkko Lehtonen, Khalifa University, UAE"},"content":{"rendered":"\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n<meta charset=\"UTF-8\">\n<meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n<title>Seminar Announcement \u2014 Mathematics Research Center<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&#038;family=DM+Mono:wght@300;400;500&#038;family=Outfit:wght@300;400;500;600&#038;display=swap\" rel=\"stylesheet\">\n<script>MathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n<style>\n  body { background: #eee; 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Instead of the binary classification into associative and non-associative operations, more refined approaches for quantifying the degree of associativity or non-associativity of a binary operation have been proposed in the literature. One such method is the so-called associative spectrum, which was introduced by Cs\u00e1k\u00e1ny and Waldhauser in 2000. The associative spectrum of a groupoid \\(G\\) is an integer sequence whose \\(n\\)-th term equals the number of distinct term operations induced on \\(G\\) by the bracketings of \\(n\\) variables.<\/p>\n<p> In this talk, we provide a brief introduction to the associative spectrum, and give an overview on our work on the associative spectra of graph algebras and quasigroups. Graph algebras were introduced by Shallon in 1979 and provide a useful representation of directed graphs as algebras with a binary operation that is not necessarily associative. A quasigroup is a groupoid satisfying the condition that for all elements \\(a\\) and \\(b\\), there exist unique elements \\(x\\) and \\(y\\) such that \\(xa = b\\) and \\(ay = b\\). This is a generalization of groups; associativity and an identity element are not required.<\/p>\n<p>This talk is based on joint work with Tam\u00e1s Waldhauser (University of Szeged).<\/p>\n    <\/div>\n  <\/div>\n\n  <!-- Footer -->\n  <div class=\"ann-footer\">\n    <span>Mathematics Research Center \u00b7 ASOIU, Baku<\/span>\n    <a href=\"\/seminars\/\">All seminars \u2192<\/a>\n  <\/div>\n\n<\/div><!-- \/.ann-block -->\n<!-- \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n     END SEMINAR ANNOUNCEMENT\n     \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 -->\n\n\n<!-- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     BLANK TEMPLATE \u2014 copy this for new announcements\n     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 -->\n<!--\n\n<div class=\"ann-block\" data-type=\"general\">\n\n  <div class=\"ann-topbar\"><\/div>\n\n  <div class=\"ann-logo-row\">\n    <img decoding=\"async\" class=\"ann-logo\" src=\"LOGO_URL_HERE\" alt=\"ASOIU Mathematics Research Center\">\n  <\/div>\n\n  <div class=\"ann-poster\">\n    <div class=\"ann-type\">General Seminar<\/div>\n    <div class=\"ann-poster-rule\"><\/div>\n    <div class=\"ann-title\">\n      TALK TITLE HERE\n    <\/div>\n    <div class=\"ann-speaker\">Speaker Name<\/div>\n    <div class=\"ann-affil\">Institution<\/div>\n  <\/div>\n\n  <div class=\"ann-meta\">\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M7 0H2a1 1 0 00-1 1v2h14V1a1 1 0 00-1-1H7zm7 4H1v10a1 1 0 001 1h12a1 1 0 001-1V4z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Date&nbsp;<\/span>Month DD, YYYY<\/span>\n    <\/div>\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 1a5 5 0 100 10A5 5 0 008 1zM0 8a8 8 0 1116 0A8 8 0 010 8z\"\/><path d=\"M7.5 4.5v4l2.5 1.5.5-.87L8.5 8V4.5z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Time&nbsp;<\/span>HH:MM<\/span>\n    <\/div>\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 0C5.24 0 3 2.24 3 5c0 3.75 5 11 5 11s5-7.25 5-11c0-2.76-2.24-5-5-5zm0 7.5a2.5 2.5 0 110-5 2.5 2.5 0 010 5z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Location&nbsp;<\/span>Room \/ Online<\/span>\n    <\/div>\n  <\/div>\n\n  <div class=\"ann-abstract\">\n    <div class=\"ann-abstract-label\">Abstract<\/div>\n    <div class=\"ann-abstract-body\">\n      <p>Abstract text here. Use \\(...\\) for inline math.<\/p>\n    <\/div>\n  <\/div>\n\n  <div class=\"ann-footer\">\n    <span>Mathematics Research Center \u00b7 ASOIU, Baku<\/span>\n    <a href=\"\/seminars\/\">All seminars \u2192<\/a>\n  <\/div>\n\n<\/div>\n\n-->\n\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Seminar Announcement \u2014 Mathematics Research Center General Seminar The associative spectrum of a binary operation Erkko Lehtonen Khalifa University, UAE Date&nbsp;December 18, 2025 Time&nbsp;14:00 Location&nbsp;MRC @ UFAZ 101 Abstract Associativity is a well-known property of some binary operations (or the corresponding groupoids). Instead of the binary classification into associative and non-associative operations, more refined approaches [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_edit_lock":["1777606059:1"],"_edit_last":["1"],"_wp_page_template":["default"],"_wp_old_date":["2026-04-17"]},"categories":[6],"tags":[24],"class_list":["post-241","post","type-post","status-publish","format-standard","hentry","category-generalseminar","tag-algebra"],"_links":{"self":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/comments?post=241"}],"version-history":[{"count":1,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/241\/revisions"}],"predecessor-version":[{"id":242,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/241\/revisions\/242"}],"wp:attachment":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/media?parent=241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/categories?post=241"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/tags?post=241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}