Estimating Statistics on Words Using Ambiguous Descriptions

Cyril Nicaud (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this article we propose an alternative way to prove some recent results on statistics on words, such as the expected number of runs or the expected sum of the run exponents. Our approach consists in designing a general framework, based on the symbolic method developed in analytic combinatorics. The descriptions obtained in this framework are built in such a way that the degree of ambiguity of an object O (i.e., the number of different descriptions corresponding to O) is exactly the value of the statistic under study for O. The asymptotic estimation of the expectation is then done using classical techniques from analytic combinatorics. To show the generality of our method, we not only apply it to obtain new proofs of known results, but also extend them from the uniform distribution to any memoryless distribution.

Mots clés: random words; runs; symbolic method; analytic combinatorics

Domaines: Combinatoire [math.CO]; Théorie et langage formel [cs.FL]

Cyril Nicaud. Estimating Statistics on Words Using Ambiguous Descriptions. 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), Jun 2016, Tel Aviv, Israel. pp.9, ⟨10.4230/LIPIcs.CPM.2016.9⟩. ⟨hal-01769095⟩