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Intertwining numbers; the n -rowed shapes

Hyoung J. Ko, Kyoung J. Lee (2007)

Czechoslovak Mathematical Journal

A fairly old problem in modular representation theory is to determine the vanishing behavior of the H o m groups and higher E x t groups of Weyl modules and to compute the dimension of the / ( p ) -vector space H o m A ¯ r ( K ¯ λ , K ¯ μ ) for any partitions λ , μ of r , which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups H o m A ¯ r ( K ¯ λ , K ¯ μ ) and provide a new formula for the intertwining number for any...

Introduction

(2004)

Commentationes Mathematicae Universitatis Carolinae

Invariance groups of finite functions and orbit equivalence of permutation groups

Eszter K. Horváth, Géza Makay, Reinhard Pöschel, Tamás Waldhauser (2015)

Open Mathematics

Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...

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