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arXiv · 1011.2409

A Unified Combinatorial Approach to Several Poincare Series Identities

Paul Levande
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Abstract

Mendes recently conjectured an identity simplifying the Poincaré series of the space of equivariant polynomial maps from $\mathbb{R}^{n}$ to a subrepresentation of $Sym^{2}(\mathbb{R}^{n})$. We show how to prove this identity using a fairly simple integer partition bijection. First, we give a bijective proof of a similar, well-known identity from representation theory. We then show that this bijection can be generalized to prove other Poincaré series identities, including a version of the identity conjectured by Mendes as well as refinements of it.

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Paul Levande. 2010-11-11. A Unified Combinatorial Approach to Several Poincare Series Identities. https://arxiv.org/abs/1011.2409

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