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OP-8764Status unassessedAnalysis

Combinatorics and Graph Theory · Question 1

Stability, hyperbolicity, and zero localization of functions · Historical workshop question

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓
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Problem statement

  • Is it true that
α:=lim inf⁡nlog⁡μ2n2n>−∞ ?\alpha:=\liminf_n \frac{\log\mu_{2n}}{2n}>-\infty \text{ ?}
  • Estimate μ2n\mu_{2n}.

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Background

Workshop introduction

A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.

Question context

Let S2nS_{2n} be the convex hull of all adjacency matrices of perfect matchings. Let

μ2n:=min⁡{haf(B):B∈S2n},\mu_{2n}:=\min\{ \text{haf}(B):B\in S_{2n}\},

where

haf(B):=1n!2n∂∂x1⋯∂x2n(xTBx)n\text{haf}(B):=\frac{1}{n!2^n}\frac{\partial}{\partial x_1\cdots\partial x_{2n}}(x^{T}Bx)^n

is the hafnian of BB.

Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

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References
  1. [1]Stability, hyperbolicity, and zero localization of functions link

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