Results 11 to 20 of about 75 (72)
Maximum entropy and integer partitions [PDF]
, 2023 We derive asymptotic formulas for the number of integer partitions with given sums of \(j\)th powers of the parts for \(j\) belonging to a finite, non-empty set \(J \subset \mathbb N\).
McKinley, Gweneth +2 more
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A family of partitions with attached parts and 'N copies of N' [PDF]
, 2015 in this paper we find two distinct combinatorial interpretations for a family of summations with several free parameters. In one case we used partitions with attached parts and in the other partitions with 'N copies of N'.
Mondek, P, Santos, JPO
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New congruences Modulo 5 and 9 for partitions with odd parts distinct [PDF]
, 2021 Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established.
Xue, Fanggang +2 more
core
Cyclic sums, network sharing, and restricted edge cuts in graphs with long cycles [PDF]
, 2007 Cyclic Sums, Network Sharing and Restricted Edge Cuts in Graphs with Long Cycles Dieter Rautenbach , Lutz Volkmann Preprint series: 07-06, 8 MSC 2000 05A17 Partitions of integers 05C40 Connectivity Abstract We study graphs G = (V,E ...
Rautenbach, Dieter, Volkmann, Lutz
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Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Open Mathematics, 2019 Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined ...
Liu Eric H., Du Wenjing
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A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
Forum of Mathematics, Sigma, 2019 Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts.
DANIEL M. KANE, ROBERT C. RHOADES
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A Combinatorial proof of a partition identity of Andrews and Stanley
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 47, Page 2495-2501, 2004., 2004 In his paper, “On a partition function of Richard Stanley,” George Andrews proves a certain partition identity analytically and asks for a combinatorial proof.This paper provides the requested combinatorial proof.
Andrew V. Sills
wiley +1 more source
Computational proofs of congruences for 2‐colored Frobenius partitions
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 333-340, 2002., 2002 In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2‐colored Frobenius partitions of n: for all n ≥ 0 and α ≥ 1, cΦ2(5αn + λα) ≡ 0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four cases of this family are proved.
Dennis Eichhorn, James A. Sellers
wiley +1 more source
n‐Color partitions with weighted differences equal to minus two
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 759-768, 1997., 1997 In this paper we study those n‐color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables.
A. K. Agarwal, R. Balasubrananian
wiley +1 more source
A Note on Graph Burning of Path Forests [PDF]
Discrete Mathematics & Theoretical Computer ScienceGraph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order $
Ta Sheng Tan, Wen Chean Teh
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