Matches in SemOpenAlex for { <https://semopenalex.org/work/W3165659239> ?p ?o ?g. }
Showing items 1 to 96 of
96
with 100 items per page.
- W3165659239 endingPage "112882" @default.
- W3165659239 startingPage "112882" @default.
- W3165659239 abstract "Let π=π1π2…πn be a permutation in the symmetric group Sn written in one-line notation. The pinnacle set of π, denoted Pin π, is the set of all πi such that πi−1<πi>πi+1. This is an analogue of the well-studied peak set of π where one considers values rather than positions. The pinnacle set was so named by Davis, Nelson, Petersen, and Tenner who showed that it has many interesting properties. In particular, they proved that the number of subsets of [n]={1,2,…,n} which can be the pinnacle set of some permutation is a binomial coefficient. Their proof involved a bijection with lattice paths and was somewhat involved. We give a simpler demonstration of this result which does not need lattice paths. Moreover, we show that our map and theirs are different descriptions of the same function. Davis et al. also studied the number of pinnacle sets with maximum m and cardinality d which they denoted by p(m,d). We show that these integers are ballot numbers and give two proofs of this fact: one using finite differences and one bijective. Diaz-Lopez, Harris, Huang, Insko, and Nilsen found a summation formula for calculating the number of permutations in Sn having a given pinnacle set. We derive a new expression for this number which is faster to calculate in many cases. We also show how this method can be adapted to find the number of orderings of a pinnacle set which can be realized by some π∈Sn." @default.
- W3165659239 created "2021-06-07" @default.
- W3165659239 creator A5012757181 @default.
- W3165659239 creator A5013956635 @default.
- W3165659239 creator A5018389489 @default.
- W3165659239 creator A5044944038 @default.
- W3165659239 creator A5061589632 @default.
- W3165659239 creator A5070369805 @default.
- W3165659239 date "2022-07-01" @default.
- W3165659239 modified "2023-10-18" @default.
- W3165659239 title "Pinnacle set properties" @default.
- W3165659239 cites W2078309700 @default.
- W3165659239 cites W2612667993 @default.
- W3165659239 cites W2808458304 @default.
- W3165659239 cites W3151839136 @default.
- W3165659239 cites W3156560627 @default.
- W3165659239 cites W3194457795 @default.
- W3165659239 cites W4205229072 @default.
- W3165659239 doi "https://doi.org/10.1016/j.disc.2022.112882" @default.
- W3165659239 hasPublicationYear "2022" @default.
- W3165659239 type Work @default.
- W3165659239 sameAs 3165659239 @default.
- W3165659239 citedByCount "5" @default.
- W3165659239 countsByYear W31656592392021 @default.
- W3165659239 countsByYear W31656592392022 @default.
- W3165659239 countsByYear W31656592392023 @default.
- W3165659239 crossrefType "journal-article" @default.
- W3165659239 hasAuthorship W3165659239A5012757181 @default.
- W3165659239 hasAuthorship W3165659239A5013956635 @default.
- W3165659239 hasAuthorship W3165659239A5018389489 @default.
- W3165659239 hasAuthorship W3165659239A5044944038 @default.
- W3165659239 hasAuthorship W3165659239A5061589632 @default.
- W3165659239 hasAuthorship W3165659239A5070369805 @default.
- W3165659239 hasConcept C114614502 @default.
- W3165659239 hasConcept C118615104 @default.
- W3165659239 hasConcept C121332964 @default.
- W3165659239 hasConcept C124101348 @default.
- W3165659239 hasConcept C126322002 @default.
- W3165659239 hasConcept C14036430 @default.
- W3165659239 hasConcept C177264268 @default.
- W3165659239 hasConcept C199360897 @default.
- W3165659239 hasConcept C201645570 @default.
- W3165659239 hasConcept C204911207 @default.
- W3165659239 hasConcept C21308566 @default.
- W3165659239 hasConcept C24424167 @default.
- W3165659239 hasConcept C24890656 @default.
- W3165659239 hasConcept C2776017024 @default.
- W3165659239 hasConcept C33923547 @default.
- W3165659239 hasConcept C41008148 @default.
- W3165659239 hasConcept C509974204 @default.
- W3165659239 hasConcept C71924100 @default.
- W3165659239 hasConcept C78458016 @default.
- W3165659239 hasConcept C86803240 @default.
- W3165659239 hasConcept C87117476 @default.
- W3165659239 hasConceptScore W3165659239C114614502 @default.
- W3165659239 hasConceptScore W3165659239C118615104 @default.
- W3165659239 hasConceptScore W3165659239C121332964 @default.
- W3165659239 hasConceptScore W3165659239C124101348 @default.
- W3165659239 hasConceptScore W3165659239C126322002 @default.
- W3165659239 hasConceptScore W3165659239C14036430 @default.
- W3165659239 hasConceptScore W3165659239C177264268 @default.
- W3165659239 hasConceptScore W3165659239C199360897 @default.
- W3165659239 hasConceptScore W3165659239C201645570 @default.
- W3165659239 hasConceptScore W3165659239C204911207 @default.
- W3165659239 hasConceptScore W3165659239C21308566 @default.
- W3165659239 hasConceptScore W3165659239C24424167 @default.
- W3165659239 hasConceptScore W3165659239C24890656 @default.
- W3165659239 hasConceptScore W3165659239C2776017024 @default.
- W3165659239 hasConceptScore W3165659239C33923547 @default.
- W3165659239 hasConceptScore W3165659239C41008148 @default.
- W3165659239 hasConceptScore W3165659239C509974204 @default.
- W3165659239 hasConceptScore W3165659239C71924100 @default.
- W3165659239 hasConceptScore W3165659239C78458016 @default.
- W3165659239 hasConceptScore W3165659239C86803240 @default.
- W3165659239 hasConceptScore W3165659239C87117476 @default.
- W3165659239 hasIssue "7" @default.
- W3165659239 hasLocation W31656592391 @default.
- W3165659239 hasOpenAccess W3165659239 @default.
- W3165659239 hasPrimaryLocation W31656592391 @default.
- W3165659239 hasRelatedWork W132200507 @default.
- W3165659239 hasRelatedWork W1567977152 @default.
- W3165659239 hasRelatedWork W1828710639 @default.
- W3165659239 hasRelatedWork W1974527570 @default.
- W3165659239 hasRelatedWork W2030171229 @default.
- W3165659239 hasRelatedWork W2083685161 @default.
- W3165659239 hasRelatedWork W2113209621 @default.
- W3165659239 hasRelatedWork W2242573402 @default.
- W3165659239 hasRelatedWork W2502624504 @default.
- W3165659239 hasRelatedWork W3165659239 @default.
- W3165659239 hasVolume "345" @default.
- W3165659239 isParatext "false" @default.
- W3165659239 isRetracted "false" @default.
- W3165659239 magId "3165659239" @default.
- W3165659239 workType "article" @default.