[KAIST Discrete Math Seminar] 12/2 *WED* 4PM (Uwe Schauz, King Fahd University of Petroleum and Minerals)

[Sang-il Oum]

***** KAIST Discrete Math Seminar *****

DATE: Dec 2, Wednesday ***UNUSUAL TIME***

TIME: 4PM-5PM

PLACE: E6-1, ROOM 1409

SPEAKER: Uwe Schauz, King Fahd University of Petroleum and Minerals,
Dhahran, Saudi Arabia

TITLE:Describing Polynomials as Equivalent to Explicit Solutions

http://mathsci.kaist.ac.kr/~sangil/seminar/entry/20091202/

We present a coefficient formula which provides some information about
the polynomial map $P|_{I_1\times\cdots\times I_n}$ when only
incomplete information about a polynomial $P(X_1,\ldots,X_n)$ is
given. It is an integrative generalization and sharpening of several
known results and has many applications, among these are:

1. The fact that polynomials $P(X_1)\neq 0$ in just one variable have
at most deg(P) roots.
2. Alon and Tarsi’s Combinatorial Nullstellensatz.
3. Chevalley and Warning’s Theorem about the number of simultaneous
zeros of systems of polynomials over finite fields.
4. Ryser’s Permanent Formula.
5. Alon’s Permanent Lemma.
6. Alon and Tarsi’s Theorem about orientations and colorings of graphs.
7. Scheim’s formula for the number of edge n-colorings of planar
n-regular graphs.
8. Alon, Friedland and Kalai’s Theorem about regular subgraphs.
9. Alon and Füredi’s Theorem about cube covers.
10. Cauchy and Davenport’s Theorem from additive number theory.
11. Erdős, Ginzburg and Ziv’s Theorem from additive number theory.