Matches in SemOpenAlex for { <https://semopenalex.org/work/W3099722123> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W3099722123 endingPage "112213" @default.
- W3099722123 startingPage "112213" @default.
- W3099722123 abstract "A polyomino is a finite, edge-connected set of cells in the plane. At the present time, an enumeration of all polyominoes is nowhere in sight. On the other hand, there are several subsets of polyominoes for which generating functions are known. For example, there exists extensive knowledge about column-convex polyominoes, a model introduced by Temperley in 1956. While studying column-convex polyominoes, researchers also gave a look at diagonally convex polyominoes (DCPs), but noticed an awkward feature: when the last diagonal of a DCP is deleted, the remaining object is not always a polyomino. So researchers focused their attention on directed DCPs. (A directed DCP is such a DCP that remains a polyomino when, for any i, its last i diagonals are deleted.) Directed DCPs gradually became well understood, whereas general DCPs have remained unexplored up to now. In this paper, we finally face general DCPs. Modulo a little trick, which saves us from dealing with non-polyominoes, we use the layered approach (described in chapter 3 of the book “Polygons, Polyominoes and Polycubes”, edited by Anthony Guttmann). The computations are of remarkable bulk. Our main result is the perimeter generating function for DCPs; we denote it D(d,x). The function D(d,x) is algebraic and satisfies an equation of degree eight. The formula for D(d,x) is about three pages long. That formula involves nine polynomials in d and x, and each of those polynomials is of degree 58 or more in x." @default.
- W3099722123 created "2020-11-23" @default.
- W3099722123 creator A5059471740 @default.
- W3099722123 date "2021-02-01" @default.
- W3099722123 modified "2023-09-26" @default.
- W3099722123 title "The perimeter generating function for nondirected diagonally convex polyominoes" @default.
- W3099722123 cites W1999694873 @default.
- W3099722123 cites W2004056472 @default.
- W3099722123 cites W2014831433 @default.
- W3099722123 cites W2036252950 @default.
- W3099722123 cites W2043788572 @default.
- W3099722123 cites W2066486509 @default.
- W3099722123 cites W2076366207 @default.
- W3099722123 doi "https://doi.org/10.1016/j.disc.2020.112213" @default.
- W3099722123 hasPublicationYear "2021" @default.
- W3099722123 type Work @default.
- W3099722123 sameAs 3099722123 @default.
- W3099722123 citedByCount "0" @default.
- W3099722123 crossrefType "journal-article" @default.
- W3099722123 hasAuthorship W3099722123A5059471740 @default.
- W3099722123 hasBestOaLocation W30997221232 @default.
- W3099722123 hasConcept C112680207 @default.
- W3099722123 hasConcept C114614502 @default.
- W3099722123 hasConcept C118615104 @default.
- W3099722123 hasConcept C130367717 @default.
- W3099722123 hasConcept C14036430 @default.
- W3099722123 hasConcept C204911207 @default.
- W3099722123 hasConcept C2524010 @default.
- W3099722123 hasConcept C33923547 @default.
- W3099722123 hasConcept C69919132 @default.
- W3099722123 hasConcept C78458016 @default.
- W3099722123 hasConcept C86803240 @default.
- W3099722123 hasConcept C98503990 @default.
- W3099722123 hasConceptScore W3099722123C112680207 @default.
- W3099722123 hasConceptScore W3099722123C114614502 @default.
- W3099722123 hasConceptScore W3099722123C118615104 @default.
- W3099722123 hasConceptScore W3099722123C130367717 @default.
- W3099722123 hasConceptScore W3099722123C14036430 @default.
- W3099722123 hasConceptScore W3099722123C204911207 @default.
- W3099722123 hasConceptScore W3099722123C2524010 @default.
- W3099722123 hasConceptScore W3099722123C33923547 @default.
- W3099722123 hasConceptScore W3099722123C69919132 @default.
- W3099722123 hasConceptScore W3099722123C78458016 @default.
- W3099722123 hasConceptScore W3099722123C86803240 @default.
- W3099722123 hasConceptScore W3099722123C98503990 @default.
- W3099722123 hasIssue "2" @default.
- W3099722123 hasLocation W30997221231 @default.
- W3099722123 hasLocation W30997221232 @default.
- W3099722123 hasOpenAccess W3099722123 @default.
- W3099722123 hasPrimaryLocation W30997221231 @default.
- W3099722123 hasRelatedWork W1586939133 @default.
- W3099722123 hasRelatedWork W1840852387 @default.
- W3099722123 hasRelatedWork W1997500179 @default.
- W3099722123 hasRelatedWork W2122003066 @default.
- W3099722123 hasRelatedWork W2156615285 @default.
- W3099722123 hasRelatedWork W2886225576 @default.
- W3099722123 hasRelatedWork W2963487007 @default.
- W3099722123 hasRelatedWork W3099722123 @default.
- W3099722123 hasRelatedWork W4288283067 @default.
- W3099722123 hasRelatedWork W82127606 @default.
- W3099722123 hasVolume "344" @default.
- W3099722123 isParatext "false" @default.
- W3099722123 isRetracted "false" @default.
- W3099722123 magId "3099722123" @default.
- W3099722123 workType "article" @default.