Sarah Barter Bailey (1935–2015)

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چکیده

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Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...

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Barter models ∗

This paper presents a family of models that involve a pair of actors that aim at bartering the goods from two privately owned pools of heterogeneous goods. The barter can occur only once or can be a repeated process with possibilities of retaliation and can involve either a single good or a basket of goods from each actor. We are indeed going to examine both the basic symmetric model (one-to-on...

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Shifted versions of the Bailey and well-poised Bailey lemmas

The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive mversions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers-Ramanujan identities.

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Iterative barter models

The paper presents two models of iterative barter where two players (A and B) aim at exchanging a pair of items without sharing any common scale of evaluation nor any common numerary good as the money. An item may be either a good or a chore (i. e. a bad) or a service of some kind and may “belong” to either players. In the first model every player proposes to the other a pair of items in an alt...

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ژورنال

عنوان ژورنال: Arms & Armour

سال: 2015

ISSN: 1741-6124,1749-6268

DOI: 10.1080/17416124.2015.1130901