Results 31 to 40 of about 79 (76)
Congruences involving generalized Frobenius partitions
, 1992 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 413-415, 1993.
James Sellers
wiley +1 more source
© Hindawi Publishing Corp. A COMBINATORIAL PROOF OF A PARTITION IDENTITY OF ANDREWS AND STANLEY
, 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
core
Integer partitions into diophantine pairs
, 2017 Let n, a and b be positive integers. The pair (a; b) is called an integer partition of n into Diophantine pair if n = a+b, ab+1 is a perfect square and a > b.
Bouroubi, S +4 more
core
Two congruences involving 4-cores
, 1996 . The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a4(n) denotes the number of 4-cores of n, then a4(9n+2) j 0 (mod 2) and a4(9n + 8) j 0 (mod 4).
Michael D. Hirschhorn, James A. Sellers
core
© Hindawi Publishing Corp. CONGRUENCES IN ORDERED PAIRS OF PARTITIONS
, 2003 Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank.
Richard Lewis, Paul Hammond
core
Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions. [PDF]
Ann Comb, 2023 Banerjee K, Dastidar MG.
europepmc +1 more source
On the Multiplicity of Parts in a Random Partition
, 1998 Let be a partition of an integer n chosen uniformly at random among all such partitions. Let s() be a part size chosen uniformly at random from the set of all part sizes that occur in .
Sylvie Corteel +3 more
core
Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type
, 1994 New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well ...
Peter Paule
core
Weighted cylindric partitions. [PDF]
J Algebr Comb (Dordr), 2022 Bridges W, Uncu AK.
europepmc +1 more source