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PRODID:Mathematics Seminar Calendar
BEGIN:VEVENT
UID:20191211T011536-19605@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:An introduction to q-analogues
DESCRIPTION:Speaker\: Bruce Sagan, MSU\r\nThe theory of q-analogues is important in both combinatorics and the study of hypergeometric series. Roughly speaking, the q-analogue of a mathematical object (which could be a number or a theorem or ...) is another object depending on a parameter q which reduces to the original object when q=1. This talk will be a gentle introduction to q-analogues. No background will be assumed.
LOCATION:C304 Wells Hall
DTSTART:20190904T190000Z
DTEND:20190904T195000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19605
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BEGIN:VEVENT
UID:20191211T011536-19624@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:Combinatorial interpretations of Lucas analogues
DESCRIPTION:Speaker\: Bruce Sagan, MSU\r\nThe Lucas sequence is a sequence of polynomials in $s,t$ defined recursively by $\{0\}=0$, $\{1\}=1$, and $\{n\}=s\{n-1\}+t\{n-2\}$ for $n\ge2$. On specialization of $s$ and $t$ one can recover the Fibonacci numbers, the nonnegative integers, and the $q$-integers $[n]_q$. Given a quantity which is expressed in terms of products and quotients of nonnegative integers, one obtains a Lucas analogue by replacing each factor of $n$ in the expression with $\{n\}$. It is then natural to ask if the resulting rational function is actually a polynomial in $s$ and $t$ and, if so, what it counts. Using lattice paths, we give combinatorial models for Lucas analogues of binomial coefficients. We also consider Catalan numbers and their relatives, such as those for finite Coxeter groups. This is joint work with Curtis Bennett, Juan Carrillo, and John Machacek.
LOCATION:C304 Wells Hall
DTSTART:20190911T190000Z
DTEND:20190911T195000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19624
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UID:20191211T011536-19644@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:Lucas atoms
DESCRIPTION:Speaker\: Bruce Sagan, MSU\r\n We introduce a powerful algebraic method for proving that Lucas analogues are polynomials with nonnegative coefficients. In particular, we factor a Lucas polynomial as\r\n$\{n\}=\prod_{d|n} P_d(s,t)$, where we call the polynomials $P_d(s,t)$ Lucas atoms. \r\nThis permits us to show that the Lucas analogues of the Fuss-Catalan and Fuss-Narayana numbers for all irreducible Coxeter groups are polynomials in $s,t$.\r\nUsing gamma expansions, a technique which has recently become popular in combinatorics and geometry, one can show that the Lucas atoms have a close relationship with cyclotomic polynomials $\Phi_d(q)$. \r\nCertain results about the $\Phi_d(q)$ can then be lifted to Lucas atoms.\r\nIn particular, one can prove analogues of theorems of Gauss and Lucas, deduce reduction formulas, and evaluate the $P_d(s,t)$ at various specific values of the variables. This is joint work with Jordan Tirrell based on an idea of Richard Stanley.
LOCATION:C304 Wells Hall
DTSTART:20190925T190000Z
DTEND:20190925T195000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19644
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BEGIN:VEVENT
UID:20191211T011536-19677@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:New and Old Combinatorial Identities Part I
DESCRIPTION:Speaker\: Aklilu Zeleke, MSU\r\nBinomial coefficients $n \choose k$ appear in different areas of mathematics (in Pascal's triangle, counting problems and computing probabilities to name few). There are also many identities that involve binomial coefficients. In this talk we will discuss new and old identities that represent positive integers and in some cases real numbers. These identities are derived from studying the asymptotic behavior of the roots of a generalized Fibonacci polynomial sequence\r\ngiven by $F_{j}(x)=x^{j}-...-x-1$.
LOCATION:C304 Wells Hall
DTSTART:20191016T190000Z
DTEND:20191016T195000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19677
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BEGIN:VEVENT
UID:20191211T011536-19678@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:New and Old Combinatorial Identities Part II
DESCRIPTION:Speaker\: Aklilu Zeleke, MSU\r\nUsing a probabilistic approach, we derive some interesting identities involving beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
LOCATION:C304 Wells Hall
DTSTART:20191030T190000Z
DTEND:20191030T195000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19678
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BEGIN:VEVENT
UID:20191211T011536-20695@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:Variations of cops and robbers on infinite graphs
DESCRIPTION:Speaker\: Robert Bell, MSU\r\nThe game of cops and robbers is a two player pursuit and evasion game played on a discrete graph G. We study a variation of the classical rules which leads to a different invariant when G is an infinite graph. In this variation, called "weak cops and robbers," the cops win by preventing the robber from visiting any vertex infinitely often. In the classical game, if G is connected and planar, then the cops can always win if there are at least three cops. We prove that this is true in the weak game if G is a locally finite plane graph with no vertex accumulation points.
LOCATION:C304 Wells Hall
DTSTART:20191106T200000Z
DTEND:20191106T205000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=20695
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BEGIN:VEVENT
UID:20191211T011536-20706@math.msu.edu
DTSTAMP:20191211T011536Z
SUMMARY:Cop number and edge deletion, addition, or subdivision
DESCRIPTION:Speaker\: Robert Bell, MSU\r\nWe present new and old results about the effect of edge operations on the cop number of a finite graph. \r\n This project was part of the SURIEM summer REU program in 2019 at MSU.
LOCATION:C304 Wells Hall
DTSTART:20191113T200000Z
DTEND:20191113T205000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=20706
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