Matches in SemOpenAlex for { <https://semopenalex.org/work/W2167012311> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W2167012311 abstract "The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and its solution. In this paper we consider a model of partially directed walks from the origin in the square lattice conned to a symmetric wedge dened by Y = pX, where p > 0 is an integer. We prove that the growth constant for all these models is equal to 1 + p 2, independent of the angle of the wedge. We derive a functional equation for the generating function of the model, and obtain an explicit solution when p = 1. From this we nd asymptotic formulas for the number of partially directed paths of length n in a wedge when p = 1. The functional equation is solved by a variation of the kernel method, which we call the iterated kernel method. This method appears to be similar to the obstinate kernel method used by Bousquet-M elou (see, for example (6, 7, 8)). This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to nd simple explicit expressions for them. However, in spite of this, the generating function turns out to be similar in form to Jacobi -functions, and has a natural boundary on the unit circle." @default.
- W2167012311 created "2016-06-24" @default.
- W2167012311 creator A5043988338 @default.
- W2167012311 creator A5052790968 @default.
- W2167012311 creator A5062457490 @default.
- W2167012311 date "2007-01-01" @default.
- W2167012311 modified "2023-09-26" @default.
- W2167012311 title "Partially directed paths in a symmetric wedge" @default.
- W2167012311 cites W1493641014 @default.
- W2167012311 cites W1570246745 @default.
- W2167012311 cites W1577336286 @default.
- W2167012311 cites W1586546819 @default.
- W2167012311 cites W1638872479 @default.
- W2167012311 cites W2002061065 @default.
- W2167012311 cites W2005365308 @default.
- W2167012311 cites W2027059032 @default.
- W2167012311 cites W2036252950 @default.
- W2167012311 cites W2039500254 @default.
- W2167012311 cites W2044350930 @default.
- W2167012311 cites W2058301955 @default.
- W2167012311 cites W2059560636 @default.
- W2167012311 cites W2063672317 @default.
- W2167012311 cites W2066588285 @default.
- W2167012311 cites W2067239301 @default.
- W2167012311 cites W2068406291 @default.
- W2167012311 cites W2076703708 @default.
- W2167012311 cites W2081302100 @default.
- W2167012311 cites W2089719844 @default.
- W2167012311 cites W2099761144 @default.
- W2167012311 cites W2120666517 @default.
- W2167012311 cites W2140893304 @default.
- W2167012311 cites W2197298196 @default.
- W2167012311 cites W2992937527 @default.
- W2167012311 cites W392365801 @default.
- W2167012311 cites W2076753854 @default.
- W2167012311 hasPublicationYear "2007" @default.
- W2167012311 type Work @default.
- W2167012311 sameAs 2167012311 @default.
- W2167012311 citedByCount "0" @default.
- W2167012311 crossrefType "journal-article" @default.
- W2167012311 hasAuthorship W2167012311A5043988338 @default.
- W2167012311 hasAuthorship W2167012311A5052790968 @default.
- W2167012311 hasAuthorship W2167012311A5062457490 @default.
- W2167012311 hasConcept C114614502 @default.
- W2167012311 hasConcept C121332964 @default.
- W2167012311 hasConcept C126875415 @default.
- W2167012311 hasConcept C134306372 @default.
- W2167012311 hasConcept C140479938 @default.
- W2167012311 hasConcept C142885752 @default.
- W2167012311 hasConcept C24890656 @default.
- W2167012311 hasConcept C2524010 @default.
- W2167012311 hasConcept C2781204021 @default.
- W2167012311 hasConcept C33923547 @default.
- W2167012311 hasConcept C47422493 @default.
- W2167012311 hasConcept C56863137 @default.
- W2167012311 hasConcept C62520636 @default.
- W2167012311 hasConcept C74193536 @default.
- W2167012311 hasConceptScore W2167012311C114614502 @default.
- W2167012311 hasConceptScore W2167012311C121332964 @default.
- W2167012311 hasConceptScore W2167012311C126875415 @default.
- W2167012311 hasConceptScore W2167012311C134306372 @default.
- W2167012311 hasConceptScore W2167012311C140479938 @default.
- W2167012311 hasConceptScore W2167012311C142885752 @default.
- W2167012311 hasConceptScore W2167012311C24890656 @default.
- W2167012311 hasConceptScore W2167012311C2524010 @default.
- W2167012311 hasConceptScore W2167012311C2781204021 @default.
- W2167012311 hasConceptScore W2167012311C33923547 @default.
- W2167012311 hasConceptScore W2167012311C47422493 @default.
- W2167012311 hasConceptScore W2167012311C56863137 @default.
- W2167012311 hasConceptScore W2167012311C62520636 @default.
- W2167012311 hasConceptScore W2167012311C74193536 @default.
- W2167012311 hasLocation W21670123111 @default.
- W2167012311 hasOpenAccess W2167012311 @default.
- W2167012311 hasPrimaryLocation W21670123111 @default.
- W2167012311 hasRelatedWork W1535526514 @default.
- W2167012311 hasRelatedWork W2032362780 @default.
- W2167012311 hasRelatedWork W2043678756 @default.
- W2167012311 hasRelatedWork W2053124281 @default.
- W2167012311 hasRelatedWork W2055716747 @default.
- W2167012311 hasRelatedWork W2100413408 @default.
- W2167012311 hasRelatedWork W2109730436 @default.
- W2167012311 hasRelatedWork W2124870776 @default.
- W2167012311 hasRelatedWork W2165283819 @default.
- W2167012311 hasRelatedWork W2766205984 @default.
- W2167012311 hasRelatedWork W2797843823 @default.
- W2167012311 hasRelatedWork W2951506846 @default.
- W2167012311 hasRelatedWork W2953001392 @default.
- W2167012311 hasRelatedWork W2963966866 @default.
- W2167012311 hasRelatedWork W3049472635 @default.
- W2167012311 hasRelatedWork W3103273613 @default.
- W2167012311 hasRelatedWork W3105264921 @default.
- W2167012311 hasRelatedWork W3122775449 @default.
- W2167012311 hasRelatedWork W3159864100 @default.
- W2167012311 hasRelatedWork W3205498162 @default.
- W2167012311 isParatext "false" @default.
- W2167012311 isRetracted "false" @default.
- W2167012311 magId "2167012311" @default.
- W2167012311 workType "article" @default.