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Counting tableaux with row and column bounds

โœ Scribed by C. Krattenthaler; S.G. Mohanty

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
507 KB
Volume
139
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

It is well known that the generating function for tableaux of a given skew shape with r rows where the parts in the ith row are bounded by some nondecreasing upper and lower bounds which depend on i can be written in the form of a determinant of size r. We show that the generating function for tableaux of a given skew shape with r rows and c columns where the parts in the ith row are bounded by nondecreasing upper and lower bounds which depend on i and the parts in thejth column are bounded by nondecreasing upper and lower bounds which depend on j can also be given in determinantal form. The size of the determinant now is r + 2c. We also show that determinants can be obtained when the nondecreasingness is dropped. Subsequently, analogous results are derived for (~,fl)-plane partitions.

๐Ÿ“œ SIMILAR VOLUMES

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