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ECCC
2010
87views more  ECCC 2010»
13 years 5 months ago
On the degree of symmetric functions on the Boolean cube
In this paper we study the degree of non-constant symmetric functions f : {0, 1}n → {0, 1, . . . , c}, where c ∈ N, when represented as polynomials over the real numbers. We s...
Gil Cohen, Amir Shpilka
JCT
2008
86views more  JCT 2008»
13 years 7 months ago
On distinguishing trees by their chromatic symmetric functions
Let T be an unrooted tree. The chromatic symmetric function XT , introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of T . The subtre...
Jeremy L. Martin, Matthew Morin, Jennifer D. Wagne...
COMBINATORICS
2007
105views more  COMBINATORICS 2007»
13 years 7 months ago
A Two Parameter Chromatic Symmetric Function
We introduce and develop a two-parameter chromatic symmetric function for a simple graph G over the field of rational functions in q and t , Q (q, t). We derive its expansion in ...
Ellison-Anne Williams
COMBINATORICS
2006
135views more  COMBINATORICS 2006»
13 years 7 months ago
Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions
Let h, e, and m denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition respectively. We gi...
Andrius Kulikauskas, Jeffrey B. Remmel
COMBINATORICS
2006
108views more  COMBINATORICS 2006»
13 years 7 months ago
Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative ...
Nantel Bergeron, Christophe Hohlweg, Mercedes Rosa...
ISMVL
2000
IEEE
103views Hardware» more  ISMVL 2000»
13 years 10 months ago
Experiments on FPRM Expressions for Partially Symmetric Logic Functions
This paper focuses on the fixed polarity ReedMuller (FPRM) expression of multiple-valued logic (MVL) symmetric functions. In the FPRM expression, each variable occurs in exactly o...
Svetlana N. Yanushkevich, Jon T. Butler, Gerhard W...
GECCO
2006
Springer
158views Optimization» more  GECCO 2006»
13 years 10 months ago
Properties of symmetric fitness functions
The properties of symmetric fitness functions are investigated. We show that a well-known encoding scheme inducing symmetric functions has the non-synonymous property and the sear...
Sung-Soon Choi, Yung-Keun Kwon, Byung Ro Moon
AISC
2010
Springer
13 years 12 months ago
Formal Proof of SCHUR Conjugate Function
Abstract. The main goal of our work is to formally prove the correctness of the key commands of the SCHUR software, an interactive program for calculating with characters of Lie gr...
Franck Butelle, Florent Hivert, Micaela Mayero, Fr...
VLSI
2007
Springer
14 years 1 months ago
Use of gray decoding for implementation of symmetric functions
— This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity ReedMuller (F...
Osnat Keren, Ilya Levin, Radomir S. Stankovic