Results 31 to 40 of about 74 (71)
© 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
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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
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© 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
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Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions. [PDF]
Ann Comb, 2023 Banerjee K, Dastidar MG.
europepmc +1 more source
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
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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
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Weighted cylindric partitions. [PDF]
J Algebr Comb (Dordr), 2022 Bridges W, Uncu AK.
europepmc +1 more source
Magic N-Cubes Form a Free Monoid
In this paper we prove a conjecture stated in an earlier paper [A-L]. The conjecture states that with respect to a rather natural operation, the set of N-dimensional magic cubes forms a free monoid for every integer N ? 1.
Allan Adler
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A note on the determinant of a Toeplitz-Hessenberg matrix
Special Matrices, 2013 Merca Mircea
doaj +1 more source