The Number of Terms in the Permanent and the Determinant of a Generic Circulant Matrix
Copyright policy )The Number of Terms in the Permanent and the Determinant of a Generic Circulant Matrix
Let A=(a_(ij)) be the generic n by n circulant matrix given by a_(ij)=x_(i+j), with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the determinant (resp. permanent) of A. The function p(n) is well-known and has several combinatorial interpretations. The function d(n), on the other hand, has not been studied previously. We show that when n is a prime power, d(n)=p(n). The proof uses symmetric functions.
6 pages; 1 figure
generic circulant matrix, Symmetric functions and generalizations, permanents, Linear and multilinear algebra, Exact enumeration problems, Basic linear algebra, Determinants, permanents, traces, other special matrix functions, determinant, permanent, Combinatorics, matrix theory, generating functions, 05E05, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15;05E05, other special matrix functions, 05A15, Enumerative combinatorics, Determinants
generic circulant matrix, Symmetric functions and generalizations, permanents, Linear and multilinear algebra, Exact enumeration problems, Basic linear algebra, Determinants, permanents, traces, other special matrix functions, determinant, permanent, Combinatorics, matrix theory, generating functions, 05E05, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15;05E05, other special matrix functions, 05A15, Enumerative combinatorics, Determinants
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!