Generalization of the Glauber-Lachs Formula, Charged Particle Distributions and the KNO Scaling at p Formula Collider

Generalization of Garsia’s Formula

Notice that Bk a is a sum of terms σ1σ2 . . . σk where σi ∈ Sn is a term of the ith copy of Ba. Each σi will be called an a-shuffle, because it shuffles the first a cards back into the deck. We can thus denote σi = (b(i−1)a+1, b(i−1)a+2, . . . , bia) where b(i−1)a+m = σi(m) (i.e. σi acted on the mth card of the deck). Thus, the sequence (σ1, . . . , σk) gives rise to the ka-tuple (b1, b2, . . ....

Improvements in Formula Generalization

From 01.10. to 05.10.2007, the Dagstuhl Seminar 07401 Deduction and Decision Procedures was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar are put together in this paper.

A Generalization of the Itô Formula

A Generalization of the Auslander-buchsbaum Formula

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.

A Generalization of Macmahon’s Formula

We generalize the generating formula for plane partitions known as MacMahon’s formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald’s symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon’s formula for strict plane partitions.