scholarly journals The Finite Heine Transformation and Conjugate Durfee Squares

Integers ◽  
2009 ◽  
Vol 9 (6) ◽  
Author(s):  
Michael Rowell ◽  
Ae Ja Yee
Keyword(s):  
Finite Form ◽  
Durfee Square ◽  
Durfee Squares

AbstractWe introduce the idea of a conjugate Durfee square and use it to answer a combinatorial question regarding a finite form of the Heine transformation posed by G. E. Andrews in a recent paper.

scholarly journals Multipartitions, generalized Durfee squares and affine Lie algebra characters

2002 ◽  
Vol 72 (3) ◽  
pp. 395-408 ◽  
Author(s):  
Peter Bouwknegt
Keyword(s):  
Lie Algebra ◽  
Partition Functions ◽  
Affine Lie Algebra ◽  
Higher Dimensional ◽  
Durfee Square ◽  
Durfee Squares

AbstractWe give some higher dimensional analogues of the Durfee square formula and point out their relation to dissections of multipartitions. We apply the results to write certain affine Lie algebra characters in terms of Universal Chiral Partition Functions.

Durfee squares in compositions

2018 ◽  
Vol 28 (6) ◽  
pp. 359-367 ◽  
Author(s):  
Margaret Archibald ◽  
Aubrey Blecher ◽  
Charlotte Brennan ◽  
Arnold Knopfmacher ◽  
Toufik Mansour
Keyword(s):  
Asymptotic Analysis ◽  
Generating Functions ◽  
Integer Partitions ◽  
Definition Of ◽  
Durfee Square ◽  
Durfee Squares

Abstract We study compositions (ordered partitions) of n. More particularly, our focus is on the bargraph representation of compositions which include or avoid squares of size s × s. We also extend the definition of a Durfee square (studied in integer partitions) to be the largest square which lies on the base of the bargraph representation of a composition (i.e., is ‘grounded’). Via generating functions and asymptotic analysis, we consider compositions of n whose Durfee squares are of size less than s × s. This is followed by a section on the total and average number of grounded s × s squares. We then count the number of Durfee squares in compositions of n.

Conditional and Other Functions of Forms in /-(zα(.))r/ in Abkhaz

2008 ◽  
Vol 12 (1) ◽  
pp. 57-71
Author(s):  
George Hewitt
Keyword(s):  
Historical Development ◽  
Semantic Feature ◽  
Finite Form ◽  
North West ◽  
Verbal Noun ◽  
The North ◽  
Morphological Segmentation ◽  
The Future

AbstractProtases ('if'-clauses) in the North West Caucasian language Abkhaz are mostly marked by either /-r/ or /-zα.r/, depending on the tense and/or type of verb (Stative or Dynamic) concerned. The article presents examples of this conditional usage and the role of protasis-type forms in both temporal and interrogative expressions as well as in complementiser-function. The complementisers in question share the semantic feature of irrealis with conditionals. A rhotic element is also found in the non-finite form of the Future I tense, in the Masdar (verbal noun), and in such converbs as the Purposives, the Resultative and the Future Absolute. The article attempts to link the semantic notions of futurity, potentiality, indefiniteness or general irrealis to the rhotic element and asks what might have been the historical development resulting in the forms attested today and thus their original morphological segmentation.

scholarly journals Two Enumerative Proofs of an Identity of Jacobi

1966 ◽  
Vol 15 (1) ◽  
pp. 67-71 ◽  
Author(s):  
C. Sudler
Keyword(s):  
Alternative Proof ◽  
Ferrers Graph ◽  
Image Position ◽  
Durfee Square

In (7), Wright gives an enumerative proof of an identity algebraically equivalent to that of Jacobi, namelyHere, and in the sequel, products run from 1 to oo and sums from - oo to oo unless otherwise indicated. We give here a simplified version of his argument by working directly with (1), the substitution leading to equation (3) of his paper being omitted. We then supply an alternative proof of (1) by means of a generalisation of the Durfee square concept utilising the rectangle of dimensions v by v + r for fixed r and maximal v contained in the Ferrers graph of a partition.

The development of person agreement and the cliticization of personal pronouns in Batsbi

2019 ◽  
Vol 72 (2) ◽  
pp. 275-296
Author(s):  
Yasuhiro Kojima
Keyword(s):  
Second Language ◽  
Strong Influence ◽  
Personal Pronoun ◽  
Personal Pronouns ◽  
Gender Agreement ◽  
Finite Form ◽  
Indirect Object ◽  
The Subject ◽  
Noun Class ◽  
Person Agreement

Abstract Most Nakh-Daghestanian languages have gender (or noun class) agreement in the verb, but do not have person agreement. This is the case with Chechen and Ingush, which are genetically the closest to Batsbi. Batsbi, by contrast, has developed person agreement with the subject in the verb along with gender agreement. This is assumed to be due to the strong influence of Georgian, which has long been the second language of Batsbi speakers. In Georgian, the verb shows person agreement with the subject as well as with the direct or indirect object. Present-day Batsbi, presumably inspired by the polypersonal agreement of Georgian, further develops the cliticization of non-subject personal pronouns. To put it simply, it seems as though Batsbi attempts to express what a Georgian verb may encode in a single, finite form by means of a verb and a personal pronoun that is cliticized to it.

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