Matches in SemOpenAlex for { <https://semopenalex.org/work/W2018935706> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W2018935706 endingPage "754" @default.
- W2018935706 startingPage "745" @default.
- W2018935706 abstract "Let $alpha,beta,m,n$ be positive integers. Fix a line $L:y=alpha x+beta$ and a lattice point $Q=(m,n)$ on L. It is well known that the number of lattice paths from the origin to Q which touch L only at Q is given by $frac{beta}{m+n}binom{m+n}m.$ We extend the above formula in various ways; in particular, we consider the case when $alpha$ and $beta$ are arbitrary positive reals. The key ingredient of our proof is a new variant of the cycle lemma originated by Dvoretzky and Motzkin [Duke Math. J., 14 (1947), pp. 305–313] and Raney [Trans. Amer. Math. Soc., 94 (1960), pp. 441–451]. We also include a counting formula for lattice paths lying under a cyclically shifting boundary, which generalizes a resultdue to Irving and Rattan in [J. Combin. Theory Ser. A, 116 (2009), pp. 499–514], and a counting formula for lattice paths having a given number of peaks, which contains the Narayana number as a special case." @default.
- W2018935706 created "2016-06-24" @default.
- W2018935706 creator A5068874976 @default.
- W2018935706 creator A5087581400 @default.
- W2018935706 date "2012-01-01" @default.
- W2018935706 modified "2023-09-26" @default.
- W2018935706 title "Counting Lattice Paths via a New Cycle Lemma" @default.
- W2018935706 cites W1971497686 @default.
- W2018935706 cites W2034224223 @default.
- W2018935706 cites W2070651047 @default.
- W2018935706 cites W2088132468 @default.
- W2018935706 doi "https://doi.org/10.1137/100796431" @default.
- W2018935706 hasPublicationYear "2012" @default.
- W2018935706 type Work @default.
- W2018935706 sameAs 2018935706 @default.
- W2018935706 citedByCount "5" @default.
- W2018935706 countsByYear W20189357062014 @default.
- W2018935706 countsByYear W20189357062018 @default.
- W2018935706 countsByYear W20189357062019 @default.
- W2018935706 countsByYear W20189357062023 @default.
- W2018935706 crossrefType "journal-article" @default.
- W2018935706 hasAuthorship W2018935706A5068874976 @default.
- W2018935706 hasAuthorship W2018935706A5087581400 @default.
- W2018935706 hasBestOaLocation W20189357062 @default.
- W2018935706 hasConcept C114614502 @default.
- W2018935706 hasConcept C118615104 @default.
- W2018935706 hasConcept C121332964 @default.
- W2018935706 hasConcept C18903297 @default.
- W2018935706 hasConcept C24890656 @default.
- W2018935706 hasConcept C2777759810 @default.
- W2018935706 hasConcept C2781204021 @default.
- W2018935706 hasConcept C33923547 @default.
- W2018935706 hasConcept C46757340 @default.
- W2018935706 hasConcept C86803240 @default.
- W2018935706 hasConceptScore W2018935706C114614502 @default.
- W2018935706 hasConceptScore W2018935706C118615104 @default.
- W2018935706 hasConceptScore W2018935706C121332964 @default.
- W2018935706 hasConceptScore W2018935706C18903297 @default.
- W2018935706 hasConceptScore W2018935706C24890656 @default.
- W2018935706 hasConceptScore W2018935706C2777759810 @default.
- W2018935706 hasConceptScore W2018935706C2781204021 @default.
- W2018935706 hasConceptScore W2018935706C33923547 @default.
- W2018935706 hasConceptScore W2018935706C46757340 @default.
- W2018935706 hasConceptScore W2018935706C86803240 @default.
- W2018935706 hasIssue "2" @default.
- W2018935706 hasLocation W20189357061 @default.
- W2018935706 hasLocation W20189357062 @default.
- W2018935706 hasOpenAccess W2018935706 @default.
- W2018935706 hasPrimaryLocation W20189357061 @default.
- W2018935706 hasRelatedWork W1993734719 @default.
- W2018935706 hasRelatedWork W2016308609 @default.
- W2018935706 hasRelatedWork W2042536766 @default.
- W2018935706 hasRelatedWork W2089618463 @default.
- W2018935706 hasRelatedWork W2167810763 @default.
- W2018935706 hasRelatedWork W2560350525 @default.
- W2018935706 hasRelatedWork W2603093731 @default.
- W2018935706 hasRelatedWork W2754599970 @default.
- W2018935706 hasRelatedWork W3102934840 @default.
- W2018935706 hasRelatedWork W4248657228 @default.
- W2018935706 hasVolume "26" @default.
- W2018935706 isParatext "false" @default.
- W2018935706 isRetracted "false" @default.
- W2018935706 magId "2018935706" @default.
- W2018935706 workType "article" @default.