단봉수열 (unimodal sequence)

개요

• 유한수열 \(a_0,a_1,\cdots, a_d\)을 생각하자
• 적당한 \(0\le j\le d\)가 존재하여 \(a_0\le a_1\ \cdots \le a_d \ge a_{d+1}\cdots \ge a_{d}\)을 만족하면 이를 단봉수열이라 한다

관련된 항목들

• 로그볼록수열 (log concave sequence)

매스매티카 파일 및 계산 리소스

• https://drive.google.com/file/d/0B8XXo8Tve1cxRXRFV1pYTVRTY2s/view

수학용어번역

• unimodal - 대한수학회 수학용어집

리뷰, 에세이, 강의노트

• 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

• Stanley, Richard P. 1980. “Unimodal Sequences Arising from Lie Algebras.” In Combinatorics, Representation Theory and Statistical Methods in Groups, 57:127–136. Lecture Notes in Pure and Appl. Math. New York: Dekker. http://www.ams.org/mathscinet-getitem?mr=588199.
• Hughes, J. W. B. 1977. “Lie Algebraic Proofs of Some Theorems on Partitions.” In Number Theory and Algebra, 135–155. New York: Academic Press. http://www.ams.org/mathscinet-getitem?mr=0491213.