APPLICATIONS OF INFINITE LOWER TRIANGULAR MATRICES AND THEIR GROUP STRUCTURE IN COMBINATORICS AND THE THEORY OF ORTHOGONAL POLYNOMIALS

APPLICATIONS OF INFINITE LOWER TRIANGULAR MATRICES AND THEIR GROUP STRUCTURE IN COMBINATORICS AND THE THEORY OF ORTHOGONAL POLYNOMIALS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 18 December 2025 V1 Latest version Share on APPLICATIONS OF INFINITE LOWER TRIANGULAR MATRICES AND THEIR GROUP STRUCTURE IN COMBINATORICS AND THE THEORY OF ORTHOGONAL POLYNOMIALS Authors : Paweł Szabłowski 0000-0002-3013-5163 [email protected] and Pawe×j Szab× Owski Authors Info & Affiliations https://doi.org/10.22541/au.176607198.81657601/v1 Published Utilitas Mathematica Version of record Peer review timeline 108 views 74 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Our focus is on the set of lower-triangular, in…nite matrices that have natural operations like addition, multiplication by a number, and matrix multiplication. With respect to each of these operations individually, the set preserves the group structure. The set becomes an algebra with unity when all three operations are considered together. We indicate important properties of the algebraic structures obtained in this way. In particular, we indicate several subgroups or sub-rings. Among subgroups, we consider the group of Riordan matrices and indicate its several subgroups. We show a variety of examples (approximately 20) of matrices that are composed of the sequences of important polynomial or number families as entries of certain lower-triangular in…nite matrices. New, signi…cant relationships between these families can be discovered by applying well-known matrix operations like multiplication and inverse calculation to this representation. The paper intends to compile numerous simple facts about lower-triangular matrices, speci…cally the family of Rionian matrices, and brie ‡y review their properties. Supplementary Material File (lower_triangular_mod2.pdf) Download 220.56 KB Information & Authors Information Version history V1 Version 1 18 December 2025 Peer review timeline Published Utilitas Mathematica Version of Record 27 Jan 2026 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords askey-wilson polynomials lower triangular matrix orthogonal polynomials q-series riordan matrix Authors Affiliations Paweł Szabłowski 0000-0002-3013-5163 [email protected] View all articles by this author Pawe×j Szab× Owski View all articles by this author Metrics & Citations Metrics Article Usage 108 views 74 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Paweł Szabłowski, Pawe×j Szab× Owski. APPLICATIONS OF INFINITE LOWER TRIANGULAR MATRICES AND THEIR GROUP STRUCTURE IN COMBINATORICS AND THE THEORY OF ORTHOGONAL POLYNOMIALS. Authorea . 18 December 2025. DOI: https://doi.org/10.22541/au.176607198.81657601/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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