BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bishal Deb (University College London) DTSTART:20211118T060000Z DTEND:20211118T070000Z DTSTAMP:20260423T004142Z UID:ARCSIN/7 DESCRIPTION:Title: A nalysing a strategy for a card guessing game via continuously increasing s ubsequences in multiset permutations\nby Bishal Deb (University Colleg e London) as part of ARCSIN - Algebra\, Representations\, Combinatorics an d Symmetric functions in INdia\n\n\nAbstract\nConsider the following card guessing game introduced by Diaconis and Graham (1981): there is a shuffle d deck of $mn$ cards with $n$ distinct cards numbered $1$ to $n$\, each ap pearing with multiplicity $m$. In each round\, the player has to guess the top card of the deck\, and is then told whether the guess was correct or not\, the top card is then discarded and then the game continues with the next card. This is known as the partial feedback model. The aim is to maxi mise the number of correct guesses. One possible strategy is the shifting strategy in which the player keeps guessing $1$ every round until the gues s is correct in some round\, and then keeps guessing $2$\, and then $3$ an d so on. We are interested in finding the expected score using this strate gy.\n\nWe can restate this problem as finding the expectation of the large st value of $i$ such that $123\\ldots i$ is a subsequence in a word formed using letters 1 to n where each letter occurs with multiplicity $m$. In t his talk\, we show that this number is $m+1 - 1/(m+2)$ plus an exponential error term. This confirms a conjecture of Diaconis\, Graham\, He and Spir o.\n\nThis talk will be at an interface between combinatorics\, probabilit y and analysis and will feature an unexpected appearance of the Taylor pol ynomials of the exponential function. This is based on joint work with Ale xander Clifton\, Yifeng Huang\, Sam Spiro and Semin Yoo.\n LOCATION:https://researchseminars.org/talk/ARCSIN/7/ END:VEVENT END:VCALENDAR