로그볼록수열 (log concave sequence)

개요

• 수열 \(\{a_n\}_{n}\)이 모든 \(i\geq 1\)에 대하여 \(a_i^2 \geq a_{i-1}a_{i+1}\)을 만족하면 로그볼록수열이라 한다

메모

• Armin, On multiple and infinite log-concavity

관련된 항목들

• 단봉수열 (unimodal sequence)

매스매티카 파일 및 계산 리소스

• https://drive.google.com/file/d/0B8XXo8Tve1cxeDd6dndNQnEzNms/view

수학용어번역

• log - 대한수학회 수학용어집
• concave - 대한수학회 수학용어집

리뷰, 에세이, 강의노트

• Brändén, Petter. ‘Unimodality, Log-Concavity, Real-Rootedness and beyond’. arXiv:1410.6601 [math], 24 October 2014. http://arxiv.org/abs/1410.6601.
• F. Brenti, Log-concave and Unimodal sequences in Algebra, Combinatorics, and Geometry: an update, Contemporary Math., 178 (1994), 71-89 http://www.mat.uniroma2.it/~brenti/10.dvi
• R. Stanley, Log-concave and unimodal sequences in Algebra, Combinatorics and Geometry, Annals of the New York Academy of Sciences, 576 (1989), 500-534 http://dedekind.mit.edu/~rstan/pubs/pubfiles/72.pdf

관련논문

• Petter Brändén, Iterated sequences and the geometry of zeros, arXiv:0909.1927 [math.CO], September 10 2009, http://arxiv.org/abs/0909.1927, 10.1515/CRELLE.2011.063, http://dx.doi.org/10.1515/CRELLE.2011.063, J. Reine Angew. Math. 658 (2011), 115-131
• Medina, Luis A., and Armin Straub. 2014. “On Multiple and Infinite Log-Concavity.” arXiv:1405.1765 [math], May. http://arxiv.org/abs/1405.1765.
• McNamara, Peter R. W., and Bruce E. Sagan. 2010. “Infinite Log-Concavity: Developments and Conjectures.” Advances in Applied Mathematics 44 (1): 1–15. doi:10.1016/j.aam.2009.03.001.