Order Polynomials and Pólya's Enumeration Theorem
نویسندگان
چکیده
منابع مشابه
Order Polynomials and Pólya's Enumeration Theorem
Pólya’s enumeration theorem states that the number of labelings of a finite set up to symmetry is given by a polynomial in the number of labels. We give a new perspective on this theorem by generalizing it to partially ordered sets and order preserving maps. Further we prove a reciprocity statement in terms of strictly order preserving maps generalizing a classical result by Stanley (1970). We ...
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Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, j ≤ m and ∑m j=1 nj = N , are derived. Among a vast number of counting problems one of the most popular is a necklace enumeration. A cyclic necklace is a coloring in m colors of the vertices of a regular N–gon, where two colorings are equivalent if one can be obtained from the other ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4066