{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:08:02Z","timestamp":1776488882670,"version":"3.51.2"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2013,1,11]],"date-time":"2013-01-11T00:00:00Z","timestamp":1357862400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,3]]},"abstract":"This paper is the first application of the compensation approach (a well-established theory in probability theory) to counting problems. We discuss how this method can be applied to a general class of walks in the quarter plane<\/jats:private-char>+<\/jats:sub>2<\/jats:sup>with a step set that is a subset of\\[ \\{(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)\\}\\]<\/jats:tex-math><\/jats:alternatives><\/jats:disp-formula><\/jats:disp-formula-group>in the interior of<\/jats:private-char>+<\/jats:sub>2<\/jats:sup>. We derive an explicit expression for the generating function which turns out to be non-holonomic, and which can be used to obtain exact and asymptotic expressions for the counting numbers.<\/jats:p>","DOI":"10.1017\/s0963548312000594","type":"journal-article","created":{"date-parts":[[2013,1,11]],"date-time":"2013-01-11T14:55:43Z","timestamp":1357916143000},"page":"161-183","source":"Crossref","is-referenced-by-count":6,"title":["The Compensation Approach for Walks With Small Steps in the Quarter Plane"],"prefix":"10.1017","volume":"22","author":[{"given":"IVO J. B. 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