Matches in SemOpenAlex for { <https://semopenalex.org/work/W2253733002> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W2253733002 abstract "In the past decade, a lot of attention has been devoted to the enumera-tion of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear transformation). But what about walks in non-convex cones? We investigate the two most natural cases: first, square lattice walks avoiding the negative quadrant Q 1 = {(i, j) : i textless{} 0 and j textless{} 0}, and then, square lattice walks avoiding the West quadrant Q 2 = {(i, j) : i textless{} j and i textless{} --j}. In both cases, the generating function that counts walks starting from the origin is found to differ from a simple D-finite series by an algebraic one. We also obtain closed form expressions for the number of n-step walks ending at certain prescribed endpoints, as a sum of three hypergeometric terms. One of these terms already appears in the enumeration of square lattice walks confined to the cone {(i, j) : i +j $ge$ 0 and j $ge$ 0}, known as Gessel's walks. In fact, the enumeration of Gessel's walks follows, by the reflection principle, from the enumeration of walks starting from (--1, 0) and avoiding Q 1. Their generating function turns out to be purely algebraic (as the generating function of Gessel's walks). Another approach to Gessel's walks consists in counting walks that start from (--1, 1) and avoid the West quadrant Q 2. The associated generating function is D-finite but transcendental." @default.
- W2253733002 created "2016-06-24" @default.
- W2253733002 creator A5014744803 @default.
- W2253733002 date "2015-11-06" @default.
- W2253733002 modified "2023-09-25" @default.
- W2253733002 title "Square lattice walks avoiding a quadrant" @default.
- W2253733002 cites W1512435182 @default.
- W2253733002 cites W1586546819 @default.
- W2253733002 cites W1640170699 @default.
- W2253733002 cites W1971620568 @default.
- W2253733002 cites W1979705808 @default.
- W2253733002 cites W1995705026 @default.
- W2253733002 cites W1997965066 @default.
- W2253733002 cites W1998068293 @default.
- W2253733002 cites W2023099303 @default.
- W2253733002 cites W2028350743 @default.
- W2253733002 cites W2034324189 @default.
- W2253733002 cites W2079699338 @default.
- W2253733002 cites W2083916911 @default.
- W2253733002 cites W2089719844 @default.
- W2253733002 cites W2232416236 @default.
- W2253733002 cites W2340541605 @default.
- W2253733002 cites W2949839976 @default.
- W2253733002 cites W2964180469 @default.
- W2253733002 cites W3097990754 @default.
- W2253733002 cites W3100391967 @default.
- W2253733002 cites W820108349 @default.
- W2253733002 hasPublicationYear "2015" @default.
- W2253733002 type Work @default.
- W2253733002 sameAs 2253733002 @default.
- W2253733002 citedByCount "0" @default.
- W2253733002 crossrefType "posted-content" @default.
- W2253733002 hasAuthorship W2253733002A5014744803 @default.
- W2253733002 hasConcept C105795698 @default.
- W2253733002 hasConcept C112680207 @default.
- W2253733002 hasConcept C114614502 @default.
- W2253733002 hasConcept C118615104 @default.
- W2253733002 hasConcept C121194460 @default.
- W2253733002 hasConcept C121332964 @default.
- W2253733002 hasConcept C121864883 @default.
- W2253733002 hasConcept C134306372 @default.
- W2253733002 hasConcept C142724271 @default.
- W2253733002 hasConcept C204911207 @default.
- W2253733002 hasConcept C24890656 @default.
- W2253733002 hasConcept C2524010 @default.
- W2253733002 hasConcept C2777620828 @default.
- W2253733002 hasConcept C2780639617 @default.
- W2253733002 hasConcept C2781204021 @default.
- W2253733002 hasConcept C33923547 @default.
- W2253733002 hasConcept C51329190 @default.
- W2253733002 hasConcept C71924100 @default.
- W2253733002 hasConcept C9376300 @default.
- W2253733002 hasConceptScore W2253733002C105795698 @default.
- W2253733002 hasConceptScore W2253733002C112680207 @default.
- W2253733002 hasConceptScore W2253733002C114614502 @default.
- W2253733002 hasConceptScore W2253733002C118615104 @default.
- W2253733002 hasConceptScore W2253733002C121194460 @default.
- W2253733002 hasConceptScore W2253733002C121332964 @default.
- W2253733002 hasConceptScore W2253733002C121864883 @default.
- W2253733002 hasConceptScore W2253733002C134306372 @default.
- W2253733002 hasConceptScore W2253733002C142724271 @default.
- W2253733002 hasConceptScore W2253733002C204911207 @default.
- W2253733002 hasConceptScore W2253733002C24890656 @default.
- W2253733002 hasConceptScore W2253733002C2524010 @default.
- W2253733002 hasConceptScore W2253733002C2777620828 @default.
- W2253733002 hasConceptScore W2253733002C2780639617 @default.
- W2253733002 hasConceptScore W2253733002C2781204021 @default.
- W2253733002 hasConceptScore W2253733002C33923547 @default.
- W2253733002 hasConceptScore W2253733002C51329190 @default.
- W2253733002 hasConceptScore W2253733002C71924100 @default.
- W2253733002 hasConceptScore W2253733002C9376300 @default.
- W2253733002 hasLocation W22537330021 @default.
- W2253733002 hasOpenAccess W2253733002 @default.
- W2253733002 hasPrimaryLocation W22537330021 @default.
- W2253733002 hasRelatedWork W1655533987 @default.
- W2253733002 hasRelatedWork W2051669952 @default.
- W2253733002 hasRelatedWork W2081568866 @default.
- W2253733002 hasRelatedWork W2086555146 @default.
- W2253733002 hasRelatedWork W2141240899 @default.
- W2253733002 hasRelatedWork W2367494929 @default.
- W2253733002 hasRelatedWork W2501495083 @default.
- W2253733002 hasRelatedWork W2586203351 @default.
- W2253733002 hasRelatedWork W2808592517 @default.
- W2253733002 hasRelatedWork W2945793193 @default.
- W2253733002 hasRelatedWork W2950068426 @default.
- W2253733002 hasRelatedWork W2950900896 @default.
- W2253733002 hasRelatedWork W2963194873 @default.
- W2253733002 hasRelatedWork W2963831988 @default.
- W2253733002 hasRelatedWork W3100283379 @default.
- W2253733002 hasRelatedWork W3105835323 @default.
- W2253733002 hasRelatedWork W3208954569 @default.
- W2253733002 hasRelatedWork W40610547 @default.
- W2253733002 hasRelatedWork W868410753 @default.
- W2253733002 hasRelatedWork W2161393165 @default.
- W2253733002 isParatext "false" @default.
- W2253733002 isRetracted "false" @default.
- W2253733002 magId "2253733002" @default.
- W2253733002 workType "article" @default.