Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287636928> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W4287636928 abstract "In this paper, we use techniques of enumerative combinatorics to study the following problem: we count the number of ways to split $n$ balls into nonempty, ordered bins so that the most crowded bin has exactly $k$ balls. We find closed forms for three of the different cases that can arise: $k > frac{n}{2}$, $k = frac{n}{2}$, and when there exists $j < k$ such that $n = 2k + j$. As an immediate result of our proofs, we find a closed form for the number of positive integer solutions to $x_1 + x_2 + dots + x_{ell} = n$ with the attained maximum of ${x_1, x_2, dots, x_{ell}}$ being equal to $k$, when $n$ and $k$ have one of the aforementioned algebraic relationships to each other. The problem is generalized to find a formula that enumerates the total number of ways without specific conditions on $n, ell, k$. Subsequently, various additional identities and estimates related to this enumeration are proven and interpreted." @default.
- W4287636928 created "2022-07-25" @default.
- W4287636928 creator A5003556957 @default.
- W4287636928 creator A5042081211 @default.
- W4287636928 date "2020-10-19" @default.
- W4287636928 modified "2023-09-26" @default.
- W4287636928 title "On the Combinatorics of Placing Balls into Ordered Bins" @default.
- W4287636928 doi "https://doi.org/10.48550/arxiv.2010.09599" @default.
- W4287636928 hasPublicationYear "2020" @default.
- W4287636928 type Work @default.
- W4287636928 citedByCount "0" @default.
- W4287636928 crossrefType "posted-content" @default.
- W4287636928 hasAuthorship W4287636928A5003556957 @default.
- W4287636928 hasAuthorship W4287636928A5042081211 @default.
- W4287636928 hasBestOaLocation W42876369281 @default.
- W4287636928 hasConcept C108710211 @default.
- W4287636928 hasConcept C114614502 @default.
- W4287636928 hasConcept C118615104 @default.
- W4287636928 hasConcept C134306372 @default.
- W4287636928 hasConcept C156340839 @default.
- W4287636928 hasConcept C199360897 @default.
- W4287636928 hasConcept C2524010 @default.
- W4287636928 hasConcept C33923547 @default.
- W4287636928 hasConcept C41008148 @default.
- W4287636928 hasConcept C549619432 @default.
- W4287636928 hasConcept C9376300 @default.
- W4287636928 hasConcept C97137487 @default.
- W4287636928 hasConceptScore W4287636928C108710211 @default.
- W4287636928 hasConceptScore W4287636928C114614502 @default.
- W4287636928 hasConceptScore W4287636928C118615104 @default.
- W4287636928 hasConceptScore W4287636928C134306372 @default.
- W4287636928 hasConceptScore W4287636928C156340839 @default.
- W4287636928 hasConceptScore W4287636928C199360897 @default.
- W4287636928 hasConceptScore W4287636928C2524010 @default.
- W4287636928 hasConceptScore W4287636928C33923547 @default.
- W4287636928 hasConceptScore W4287636928C41008148 @default.
- W4287636928 hasConceptScore W4287636928C549619432 @default.
- W4287636928 hasConceptScore W4287636928C9376300 @default.
- W4287636928 hasConceptScore W4287636928C97137487 @default.
- W4287636928 hasLocation W42876369281 @default.
- W4287636928 hasOpenAccess W4287636928 @default.
- W4287636928 hasPrimaryLocation W42876369281 @default.
- W4287636928 hasRelatedWork W1850102257 @default.
- W4287636928 hasRelatedWork W2018113351 @default.
- W4287636928 hasRelatedWork W2041903417 @default.
- W4287636928 hasRelatedWork W2065078642 @default.
- W4287636928 hasRelatedWork W2117618537 @default.
- W4287636928 hasRelatedWork W2327497304 @default.
- W4287636928 hasRelatedWork W2794784053 @default.
- W4287636928 hasRelatedWork W2964165395 @default.
- W4287636928 hasRelatedWork W2964273561 @default.
- W4287636928 hasRelatedWork W3093428390 @default.
- W4287636928 isParatext "false" @default.
- W4287636928 isRetracted "false" @default.
- W4287636928 workType "article" @default.