منابع مشابه
Partitions of Even Rank and Euler Numbers
This paper is based on an hour address given at the Sixth Conference on Formal Power Series and Algebraic Combinatorics, held at DIMACS in 1994. It is written primarily for an audience of combinato-rialists. Our hope is to publicise some intriguing enumerative conjectures which arise in the study of the homology representations of the poset of (set) partitions with an even number of blocks. The...
متن کاملEven Partitions in Plethysms
We prove that for all natural numbers k, n, d with k ≤ d and every partition λ of size kn with at most k parts there exists an irreducible GLd(C)-representation of highest weight 2λ in the plethysm Sym(SymC). This gives an affirmative answer to a conjecture by Weintraub (J. Algebra, 129 (1): 103-114, 1990). Our investigation is motivated by questions of geometric complexity theory and uses idea...
متن کامل0 Even Partitions in Plethysms
We prove that for all natural numbers k, n, d with k ≤ d and every partition λ of size kn with at most k parts there exists an irreducible GLd(C)-representation of highest weight 2λ in the plethysm Sym(SymC). This gives an affirmative answer to a conjecture by Weintraub (J. Algebra, 129 (1): 103-114, 1990). Our investigation is motivated by questions of geometric complexity theory and uses idea...
متن کاملCounting Even and Odd Partitions
1. Introduction. It is a lovely fact that n] = f1; 2; : : : ; ng, n 1, has as many subsets X with an even cardinality jXj as those with an odd cardinality, namely 2 n?1 of both. To prove it, pair every subset X with X 1 where X 1 is Xnf1g if 1 2 X and X f1g if 1 6 2 X. Then X 7 ! X 1 is an involution that changes the parity of jXj and the result follows. More generally, in enumerative combinato...
متن کاملPlethysm, Partitions with an Even Number of Blocks and Euler Numbers
This paper is based on an hour address given at the Sixth Conference on Formal Power Series and Algebraic Combinatorics, held at DIMACS in 1994. It is written primarily for an audience of combinatorialists. Our hope is to publicise some intriguing enumerative conjectures which arise in the study of the homology representations of the poset of (set) partitions with an even number of blocks. The ...
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ژورنال
عنوان ژورنال: New Trends in Mathematical Science
سال: 2017
ISSN: 2147-5520
DOI: 10.20852/ntmsci.2017.128