Translator Disclaimer
2012 Total positivity of a shuffle matrix
Audra McMillan
Involve 5(1): 61-65 (2012). DOI: 10.2140/involve.2012.5.61

Abstract

Holte introduced a n×n matrix P as a transition matrix related to the carries obtained when summing n numbers base b. Since then Diaconis and Fulman have further studied this matrix proving it to also be a transition matrix related to the process of b-riffle shuffling n cards. They also conjectured that the matrix P is totally nonnegative. In this paper, the matrix P is written as a product of a totally nonnegative matrix and an upper triangular matrix. The positivity of the leading principal minors for general n and b is proven as well as the nonnegativity of minors composed from initial columns and arbitrary rows.

Citation

Download Citation

Audra McMillan. "Total positivity of a shuffle matrix." Involve 5 (1) 61 - 65, 2012. https://doi.org/10.2140/involve.2012.5.61

Information

Received: 24 February 2011; Revised: 17 July 2011; Accepted: 4 September 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1252.15037
MathSciNet: MR2924314
Digital Object Identifier: 10.2140/involve.2012.5.61

Subjects:
Primary: 15B48, 60C05

Rights: Copyright © 2012 Mathematical Sciences Publishers

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.5 • No. 1 • 2012
MSP
Back to Top