English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This thesis is divided into three parts. The first part deals with cylindricplane partitions. The second with lambda-determinants and the third withcommutators in semi-circular systems. For more detailed abstract please seeinside.  Cylindric plane partitions may be thought of as a natural generalization ofreverse plane partitions. A generating series for the enumeration of cylindricplane partitions was recently given by Borodin. The first result of section oneis a new bijective proof of Borodin's identity which makes use of Fomin'sgrowth diagram framework for generalized RSK correspondences. The second resultis a $(q,t)$-analog of Borodin's identity which extends previous work by Okadain the reverse plane partition case. The third result is an explicitcombinatorial interpretation of the Macdonald weight occurring in the$(q,t)$-analog using the non-intersecting lattice path model for cylindricplane partitions.  Alternating sign matrices were discovered by Robbins and Rumsey whilststudying \emph{$\lambda$-determinants}. In the second part of this thesis weprove a multi-parameter generalization of the $\lambda$-determinant,generalizing a recent result by di Francesco. Like the original$\lambda$-determinant, our formula exhibits the \emph{Laurent phenomenon}.  Semicircular systems were first introduced by Voiculescu as a part of hisstudy of von Neumann algebras. In the third part of this thesis we studycertain commutator subalgebras of the semicircular system. We find a projectionmatrix with an interesting self-similar structure. Making use of our projectionformula we given an alternative, elementary proof that the semicircular systemis a factor.

Cylindric plane partitions, Lambda determinants, Commutants in semicircular systems