Combinatorial proofs and generalizations of conjectures related to Euler’s partition theorem
Tài liệu tham khảo
Andrews, 1998
Andrews, 2008, The number of smallest parts in the partitions of n, J. Reine Angew. Math., 624, 133
Andrews, 2017, The Bhargava-Adiga summation and partitions, J. Indian Math. Soc. (N.S.), 84, 151, 10.18311/jims/2017/15836
Andrews, 2017, Euler’s partition identity and two problems of George Beck, Math. Student, 86, 115
Chern, 2018, On a conjecture of George Beck, Int. J. Number Theory, 14, 647, 10.1142/S1793042118500392
Euler, 1748
Fokkink, 1995, A relation between partitions and the number of divisors, Amer. Math. Monthly, 102, 345, 10.1080/00029890.1995.11990581
Franklin, 1883, On partitions, Johns Hopkins Univ. Circ., 2, 72
Fu, 2017, Generalizing a partition theorem of Andrews, Math. Student, 86, 91
Glaisher, 1883, A theorem in partitions, Messenger Math., 12, 158
Pak, 2006, Partition bijections, a survey, Ramanujan J., 12, 5, 10.1007/s11139-006-9576-1
Remmel, 1982, Bijective proofs of some classical partition identities, J. Combin. Theory Ser. A, 33, 273, 10.1016/0097-3165(82)90040-1
Sylvester, 1882, A constructive theory of partitions, arranged in three acts, an interact and an exodion, Amer. J. Math., 5, 251, 10.2307/2369545
The On-Line Encyclopedia of Integer Sequences, Sequence A034296, https://oeis.org/A034296.
The On-Line Encyclopedia of Integer Sequences, Sequence A090867, https://oeis.org/A090867.
H.S. Wilf, Lectures on Integer Partitions, 2000, unpublished. Available at: https://www.math.upenn.edu/ wilf/PIMS/PIMSLectures.pdf.