{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T11:09:37Z","timestamp":1742987377995,"version":"3.40.3"},"publisher-location":"Cham","reference-count":16,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030869724"},{"type":"electronic","value":"9783030869731"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-86973-1_31","type":"book-chapter","created":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T12:03:14Z","timestamp":1631275394000},"page":"439-448","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Pascal-Like Triangle with Quaternionic Entries"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7948-8341","authenticated-orcid":false,"given":"Maria Irene","family":"Falc\u00e3o","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0830-3316","authenticated-orcid":false,"given":"Helmuth R.","family":"Malonek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,11]]},"reference":[{"issue":"1","key":"31_CR1","first-page":"295","volume":"187","author":"R Askey","year":"1974","unstructured":"Askey, R., Steinig, J., Trans. AMS: Some positive trigonometric sums 187(1), 295\u2013307 (1974)","journal-title":"Some positive trigonometric sums"},{"key":"31_CR2","unstructured":"Bondarenko, B.A.: Generalized Pascal triangles and pyramids, their fractals, graphs, and applications, volume vii. CA: The Fibonacci Association, (translated from the Russian by Richard C. Bollinger), Santa Clara (1993)"},{"key":"31_CR3","volume-title":"Clifford Analysis","author":"F Brackx","year":"1982","unstructured":"Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Pitman, Boston-London-Melbourne (1982)"},{"key":"31_CR4","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: On Vietoris\u2019 number sequence and combinatorial identities with quaternions. In: Vigo-Aguiar, J. (eds.) CMMSE 2017: 17th International Conference on Computational and Mathematical Methods in Science and Engineering, pp. 480\u2013488. Almer\u00eda (2017)"},{"issue":"5","key":"31_CR5","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1007\/s11785-017-0649-5","volume":"11","author":"I Ca\u00e7\u00e3o","year":"2017","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: Hypercomplex polynomials, vietoris\u2019 rational numbers and a related integer. Numbers Sequence. Complex Anal. Oper. Theory 11(5), 1059\u20131076 (2017)","journal-title":"Numbers Sequence. Complex Anal. Oper. Theory"},{"key":"31_CR6","unstructured":"Falc\u00e3o, M.I., Cruz, J., Malonek, H.R.: Remarks on the generation of monogenic functions. In: 17th International Conference on the Application of Computer Science and Mathematics on Architecture and Civil Engineering, Weimar (2006)"},{"key":"31_CR7","first-page":"486","volume":"5","author":"M Feinberg","year":"1967","unstructured":"Feinberg, M.: A Lucas Triangle. Fibonacci Quart. 5, 486\u2013490 (1967)","journal-title":"A Lucas Triangle. Fibonacci Quart."},{"key":"31_CR8","unstructured":"Gould, H.W.: Combinatorial identities: Table I: Intermediate techniques for summing finite series, from the seven unpublished manuscripts of H. W. Gould. edited and compiled by Jocelyn Quaintance (2010)"},{"key":"31_CR9","unstructured":"Graham, R.L., Knuth, D., E., Patashnik, O.: Concrete mathematics. 2nd edn. Addison-Wesley Publishing Company, Reading, MA (1994)"},{"key":"31_CR10","unstructured":"G\u00fcrlebeck, K., Habetha, K., Spr\u00f6\u00dfig, W.: Holomorphic functions in the plane and $$n$$-dimensional space, Birkh\u00e4user Verlag, Basel (translated from the 2006 German original) (2008)"},{"key":"31_CR11","unstructured":"Horn, M.E.: Die didaktische Relevanz des Pauli-Pascal-Dreiecks, In: Dietmar H\u00f6ttecke (eds.): Naturwissenschaftlicher Unterricht im internationalen Vergleich, Beitr\u00e4ge zur Jahrestagung der GDCP in Bern, vol. 27, pp. 557\u2013559, LIT-Verlag Dr. W. Hopf, Berlin (2007)"},{"key":"31_CR12","doi-asserted-by":"crossref","unstructured":"Malonek, R.: Power series representation for monogenic functions in $$\\mathbb{R}^{n+1}$$ based on a permutational product. Complex Variables, Theory Appl. 15, 181\u2013191 (1990)","DOI":"10.1080\/17476939008814449"},{"key":"31_CR13","unstructured":"Malonek, H.: Selected topics in hypercomplex function theory. In: Eriksson, S.-L. (eds.) Clifford algebras and potential theory, vol. 7, pp. 111\u2013150. University of Joensuu (2004)"},{"key":"31_CR14","unstructured":"Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. http:\/\/oeis.org"},{"key":"31_CR15","doi-asserted-by":"crossref","unstructured":"Ruscheweyh, St., Salinas, L.: Stable functions and Vietoris\u2019 theorem. J. Math. Anal. Appl. 291, 596\u2013604 (2004)","DOI":"10.1016\/j.jmaa.2003.11.035"},{"key":"31_CR16","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/978-3-662-24892-8_1","volume":"167","author":"L Vietoris","year":"1958","unstructured":"Vietoris, L.: \u00dcber das Vorzeichen gewisser trigonometrischer Summen. Sitzungsber. \u00d6sterr. Akad. Wiss 167, 125\u2013135 (1958)","journal-title":"Sitzungsber. \u00d6sterr. Akad. Wiss"}],"container-title":["Lecture Notes in Computer Science","Computational Science and Its Applications \u2013 ICCSA 2021"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-86973-1_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,22]],"date-time":"2022-01-22T08:05:21Z","timestamp":1642838721000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-86973-1_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030869724","9783030869731"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-86973-1_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"11 September 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCSA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science and Its Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cagliari","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 September 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccsa2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/iccsa.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Customed version of CyberChair 4","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1588","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"466","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"18","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"29% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2,5","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}