Random Young Tableaux and Combinatorial Identities
Grigori Olshanski, Amitai Regev

TL;DR
This paper derives new combinatorial identities related to infinite Young tableaux, connecting probability distributions with hypergeometric series and harmonic analysis on the symmetric group.
Contribution
It introduces novel multivariate combinatorial identities by analyzing probability distributions on infinite Young tableaux, extending previous work in harmonic analysis.
Findings
Derived identities as multivariate analogs of hypergeometric summation formulas
Calculated probabilities of entries in random Young tableaux
Established connections between combinatorics and harmonic analysis
Abstract
We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability distributions on the space of the infinite Young tableaux. Then we calculate the probability that the entry of a random tableau at a given box equals n=1,2,.... Summing these probabilities over n and equating the result to 1 we get a nontrivial identity. Our choice for the initial distributions is motivated by the recent work on harmonic analysis on the infinite symmetric group and related topics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Methods and Mixture Models · Algorithms and Data Compression · Advanced Combinatorial Mathematics
