A combinatorial approach to partitions with parts in the gaps

• Autorzy: Dennis Eichhorn
• Języki publikacji: EN

Abstrakty

EN

Many links exist between ordinary partitions and partitions with parts in the "gaps". In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let $p^_{k,m}(j,n)$ be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let $p*_{k,m}(j,n)$ be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then $p*_{k,m}(j,n)=p_{k,m}(j,n)$.

Kategorie tematyczne

• 05A19: Combinatorial identities, bijective combinatorics
• 05A17: Partitions of integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 2
• Strony: 119-133

Daty

wydano

1998

otrzymano

1996-11-26

poprawiono

1997-09-26

Twórcy

autor

Dennis Eichhorn

• Department of Mathematics, The University of Illinois, 1409 West Green Street, Urbana, Illinois 61801-2975, U.S.A.

Bibliografia

• [1] K. Alladi, Partition identities involving gaps and weights, Trans. Amer. Math. Soc. 349 (1997), 5001-5019.
• [2] K. Alladi, Partition identities involving gaps and weights - II, Ramanujan J., to appear.
• [3] K. Alladi, Weighted partition identities and applications, in: Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Vol. 1 (Allerton Park, Ill., 1995), Progr. Math. 138, Birkhäuser, Boston, 1996, 1-15.
• [4] D. Bowman, Partitions with numbers in their gaps, Acta Arith. 74 (1996), 97-105.
• [5] L. Euler, Introductio in Analysis Infinitorum, Marcum-Michaelem Bousquet, Lousannae, 1748.