Specht modules and chromatic polynomials

نویسنده

  • Norman Biggs
چکیده

An explicit formula for the chromatic polynomials of certain families of graphs, called ‘bracelets’, is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads to an effective means of calculation. MSC 2000: 05C15, 05C50.

منابع مشابه

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

متن کامل

Chromatic polynomials of some nanostars

Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most  colours, which is for a fixed graph G , a polynomial in  , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.

متن کامل

New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs

In this paper, for each graphG, we define a chain complex of graded modules over the ring of polynomials, whose graded Euler characteristic is equal to the chromatic polynomial of G. We also define a chain complex of doubly graded modules, whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of G. Both constructions use Koszul complexes, and are similar to the new K...

متن کامل

Symmetric Group Modules with Specht and Dual Specht Filtrations

The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group theory analogous to that of good filtrations and tilting modules for GLn(k). This paper is an initial attempt at such a theory. We obtain two sufficient conditi...

متن کامل

Fusion Products, Cohomology of Gln Flag Manifolds and Kostka Polynomials

This paper explains the relation between the fusion product of symmetric power sln evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring Rμ which describes the cohomology ring of the flag variety Flμ′ of GLN . The graded multiplicity spaces appearing in the decomposition of the fusion product into irreducible sln-modules are identified with the multiplicity spaces ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

متن کامل
عنوان ژورنال:
  • J. Comb. Theory, Ser. B

دوره 92  شماره 

صفحات  -

تاریخ انتشار 2004