Explicit computation of the variance of the number of maxima in hypercubes

Abstract

We present a combinatorial approach of the variance for the number of maxima in hypercubes. This leads to an explicit expression, in terms of Multiple Zeta Values, of the dominant term in the asymptotic expansion of this variance.Moreover, we get an algorithm to compute this expansion, and show that all coefficients occuring belong to the $\mathbb{Q}$-algebra generated by Multiple Zeta Values, and by Euler's constant $\gamma$.

Keywords

• maximal points
• harmonic sums
• shuffle algebra
• multiple zeta values
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]