{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:59:39Z","timestamp":1765486779118,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"],"award-info":[{"award-number":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"],"award-info":[{"award-number":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"]}]},{"name":"MOST","award":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"],"award-info":[{"award-number":["11501090","61807029","A2019501024","110-2115-M-017-002-MY2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros of row-generating polynomials is also presented.<\/jats:p>","DOI":"10.3390\/axioms11060297","type":"journal-article","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T01:43:27Z","timestamp":1655775807000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Context-Free Grammars for Several Triangular Arrays"],"prefix":"10.3390","volume":"11","author":[{"given":"Roberta Rui","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}]},{"given":"Jean","family":"Yeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 000800, Taiwan"}]},{"given":"Fuquan","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Science, Yanshan University, Qinhuangdao 066004, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0304-3975(93)90307-F","article-title":"Context-free grammars, differential operators and formal power series","volume":"117","author":"Chen","year":"1993","journal-title":"Theor. 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