FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4288734188> ?p ?o ?g. }

• W4288734188 endingPage "101919" @default.
• W4288734188 startingPage "101919" @default.
• W4288734188 abstract "A polyomino is a shape best described as a connected set of cells in the square lattice. As part of recreational mathematics, polyominoes have seen active research since the 1950s. Simultaneously, polyominoes have been investigated in statistical physics under the name “lattice animals,” mainly in regards to percolation problems. One of the main points of interest is to solve the yet unanswered question of how many different polyominoes exist. Most of the focus, so far, went to estimating the number of different polyominoes that can be made with a given fixed number of cells. Recently, there are increased efforts to discover the number of polyominoes with not only a given area, but with a given perimeter size or perimeter defect as well. Roughly speaking, the perimeter defect is a number that measures how many twists a polyomino has. Formally, the defect of a polyomino P is defined as the deviation of the perimeter size of P from the maximum possible perimeter size taken over all polyominoes of the same area as P. Interestingly, a polyomino might contain a column or row which can be “cut” out of the polyomino, then the remaining parts of the polyomino are “glued” back together along the cut, and result in a smaller polyomino with equal perimeter defect to the original. By repeating such “cut-and-glue” operations on a polyomino until all matching columns and rows have been removed, one obtains a so-called “reduced polyomino.” We expand on the efforts regarding perimeter defect and reduced polyominoes, in two directions. First, given a fixed perimeter defect, we demonstrate and prove upper and lower bounds on the width and height, as well as an upper bound on the area, of any reduced polyomino with a given perimeter defect. Second, we present an algorithm for enumerating all reduced polyominoes with a given perimeter defect, and calculate their combined generating function. From the generating function, we can extract a formula A(k)(n) for the number of polyominoes that have the fixed perimeter defect k and area n, for any n. Using our new algorithm, and in the case of k=5 some additional manual calculations, we provide closed formulae of A(k)(n), for up to k=5, as well as the generating functions for up to k=5. This is an improvement over the previously known formulae, which were known only up to k=3." @default.
• W4288734188 created "2022-07-30" @default.
• W4288734188 creator A5059958789 @default.
• W4288734188 creator A5078341911 @default.
• W4288734188 date "2023-01-01" @default.
• W4288734188 modified "2023-10-17" @default.
• W4288734188 title "Automatic generation of formulae for polyominoes with a fixed perimeter defect" @default.
• W4288734188 cites W1534927585 @default.
• W4288734188 cites W2012068660 @default.
• W4288734188 cites W2029862292 @default.
• W4288734188 cites W2055590727 @default.
• W4288734188 cites W2312413878 @default.
• W4288734188 cites W2318992725 @default.
• W4288734188 cites W2327692812 @default.
• W4288734188 cites W2417863416 @default.
• W4288734188 cites W2465012772 @default.
• W4288734188 cites W4213044019 @default.
• W4288734188 doi "https://doi.org/10.1016/j.comgeo.2022.101919" @default.
• W4288734188 hasPublicationYear "2023" @default.
• W4288734188 type Work @default.
• W4288734188 citedByCount "1" @default.
• W4288734188 countsByYear W42887341882022 @default.
• W4288734188 crossrefType "journal-article" @default.
• W4288734188 hasAuthorship W4288734188A5059958789 @default.
• W4288734188 hasAuthorship W4288734188A5078341911 @default.
• W4288734188 hasBestOaLocation W42887341881 @default.
• W4288734188 hasConcept C112680207 @default.
• W4288734188 hasConcept C114614502 @default.
• W4288734188 hasConcept C118615104 @default.
• W4288734188 hasConcept C121332964 @default.
• W4288734188 hasConcept C24890656 @default.
• W4288734188 hasConcept C2524010 @default.
• W4288734188 hasConcept C2781204021 @default.
• W4288734188 hasConcept C33923547 @default.
• W4288734188 hasConcept C69919132 @default.
• W4288734188 hasConcept C98503990 @default.
• W4288734188 hasConceptScore W4288734188C112680207 @default.
• W4288734188 hasConceptScore W4288734188C114614502 @default.
• W4288734188 hasConceptScore W4288734188C118615104 @default.
• W4288734188 hasConceptScore W4288734188C121332964 @default.
• W4288734188 hasConceptScore W4288734188C24890656 @default.
• W4288734188 hasConceptScore W4288734188C2524010 @default.
• W4288734188 hasConceptScore W4288734188C2781204021 @default.
• W4288734188 hasConceptScore W4288734188C33923547 @default.
• W4288734188 hasConceptScore W4288734188C69919132 @default.
• W4288734188 hasConceptScore W4288734188C98503990 @default.
• W4288734188 hasFunder F4320320950 @default.
• W4288734188 hasFunder F4320322252 @default.
• W4288734188 hasLocation W42887341881 @default.
• W4288734188 hasOpenAccess W4288734188 @default.
• W4288734188 hasPrimaryLocation W42887341881 @default.
• W4288734188 hasRelatedWork W1586939133 @default.
• W4288734188 hasRelatedWork W2052932497 @default.
• W4288734188 hasRelatedWork W2060983500 @default.
• W4288734188 hasRelatedWork W2774905398 @default.
• W4288734188 hasRelatedWork W2886225576 @default.
• W4288734188 hasRelatedWork W2911137868 @default.
• W4288734188 hasRelatedWork W3049670187 @default.
• W4288734188 hasRelatedWork W4286406563 @default.
• W4288734188 hasRelatedWork W4288734188 @default.
• W4288734188 hasRelatedWork W82127606 @default.
• W4288734188 hasVolume "108" @default.
• W4288734188 isParatext "false" @default.
• W4288734188 isRetracted "false" @default.
• W4288734188 workType "article" @default.