Minimum supports of functions on the Hamming graphs with spectral constraints

Alexandr Valyuzhenich, Konstantin Vorob'ev

Результат исследования: Научные публикации в периодических изданияхстатья

5 Цитирования (Scopus)

Аннотация

We study functions defined on the vertices of the Hamming graphs H(n,q). The adjacency matrix of H(n,q) has n+1 distinct eigenvalues n(q−1)−q⋅i with corresponding eigenspaces Ui(n,q) for 0≤i≤n. In this work, we consider the problem of finding the minimum possible support (the number of nonzeros) of functions belonging to a direct sum Ui(n,q)⊕Ui+1(n,q)⊕⋯⊕Uj(n,q) for 0≤i≤j≤n. For the case i+j≤n and q≥3 we find the minimum cardinality of the support of such functions and obtain a characterization of functions with the minimum cardinality of the support. In the case i+j>n and q≥4 we also find the minimum cardinality of the support of functions, and obtain a characterization of functions with the minimum cardinality of the support for i=j, i>[Formula presented] and q≥5. In particular, we characterize eigenfunctions from the eigenspace Ui(n,q) with the minimum cardinality of the support for cases i≤[Formula presented], q≥3 and i>[Formula presented], q≥5.

Язык оригиналаанглийский
Страницы (с-по)1351-1360
Число страниц10
ЖурналDiscrete Mathematics
Том342
Номер выпуска5
DOI
СостояниеОпубликовано - 1 мая 2019

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