Andrew SillsAffiliation: Georgia Southern University Email: asills@georgiasouthern.edu Title Of Talk: A Partition Bijection Relating the Rogers-Selberg identities to a Special Case of Gordon's Theorem URL: http://math.georgiasouthern.edu/~asills/AGRS/AGRS.pdf Abstract: Let A(n) denote the number of partitions of n such that if 2j is the largest repeated even part, then all positive even integers less than 2j also appear at least twice, no odd part less than 2j appears, and no part greater than 2j is repeated. Let G(n) denote the number of partitions of n such that 1 appears at most once, no part appears more than twice, and if j appears twice, then neither j-1 nor j+1 appear. Let C(n) denote the number of partitions of n into parts not congruent to 0, 2, or 5 modulo 7. A special case of Basil Gordon's combinatorial of the Rogers-Ramanujan identities (Amer. J. Math. 83 (1961) 393--399) asserts that G(n) = C(n) for all integers n. In "Partitions with initial repetitions" (preprint, 2006), Andrews interprets one of the Rogers-Selberg mod 7 identities as A(n) = C(n). I will present a bijection between the partitions enumerated by A(n) and those enumerated by G(n). This material is discussed in my paper, "A partition bijection related to the Rogers-Selberg identities and Gordon's theorem," Journal of Combinatorial Theory, Series A 115/1 (2008) 67-83.
Last update made Wed Mar 19 15:39:20 EDT 2008.
|