Complex roots of chromatic polynomials

1 hour 9 mins 16 secs, 957.94 MB, MPEG-4 Video 480x360, 25.0 fps, 44100 Hz, 1.84 Mbits/sec

About this item

Description:	Biggs, N (London School of Economics) Friday 25 January 2008, 10:00-11:00 Zeros of Graph Polynomials

Created:

2008-02-08 14:23

Collection:

Combinatorics and Statistical Mechanics

Publisher:

Isaac Newton Institute

Biggs, N

Language:

eng (English)

Credits:

Author:

Biggs, N


Abstract:	I shall begin by explaining how the theory of representations of the symmetric group can be applied to the transfer matrix. This leads to explicit formulae for the chromatic polynomials of families of graphs, in which the terms correspond to partitions of positive integers. The formulae are well-suited to the application of the Beraha-Kahane-Weiss theorem, describing the limit points of zeros of the polynomials. In simple cases the individual terms can be written explicitly as powers of polynomials, and the resulting limit curves are (parts of) closed curves. In the general case the curves can have end-points and singularities, and I shall discuss some of the interesting phenomena that can occur.

Abstract:

I shall begin by explaining how the theory of representations of the symmetric group can be applied to the transfer matrix. This leads to explicit formulae for the chromatic polynomials of families of graphs, in which the terms correspond to partitions of positive integers.

The formulae are well-suited to the application of the Beraha-Kahane-Weiss theorem, describing the limit points of zeros of the polynomials. In simple cases the individual terms can be written explicitly as powers of polynomials, and the resulting limit curves are (parts of) closed curves. In the general case the curves can have end-points and singularities, and I shall discuss some of the interesting phenomena that can occur.

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video *	480x360	1.84 Mbits/sec	957.94 MB	View	Download
Flash Video	480x360	807.25 kbits/sec	410.13 MB	View	Download
iPod Video	480x360	505.33 kbits/sec	256.74 MB	View	Download
Windows Media Video (for download)	480x360	479.01 kbits/sec	243.36 MB	View	Download
Windows Media Video (for streaming)	480x360	447.34 kbits/sec	227.28 MB	View	Download	Stream
RealMedia	480x360	878.78 kbits/sec	446.47 MB	View	Download	Stream
QuickTime (for download)	384x288	848.9 kbits/sec	431.29 MB	View	Download
QuickTime (for streaming)	480x360	908.09 kbits/sec	461.36 MB	View	Download
MP3	44100 Hz	125.01 kbits/sec	63.30 MB	Listen	Download