Zobrazeno 1 - 10 of 341 pro vyhledávání: '"Leonard Carlitz"'
5
Enumeration of rectangular arrays by length and coincidences
Autor: Leonard Carlitz
Publikováno v: Annali di Matematica Pura ed Applicata. 99:155-182
Explicit formulas are obtained for the number of p-line arrays of integers (aij) (i=1, 2, ..., p; j=1, 2, ..., n) satisfying 1=ap1=...=a11⩽ap2⩽...a12⩽...⩽apn⩽...⩽a1n and a1j⩽j (j=1, 2, ..., n) and having k coincidences. (A coincidence i
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e2cfe85ac0cf3858ac01724c04df13dd
https://doi.org/10.1007/bf02413723
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6
Enumeration of pairs of permutations
Autor: Leonard Carlitz, Richard Scoville, Theresa P. Vaughan
Publikováno v: Discrete Mathematics. 14(3):215-239
Let @p = (a"1, a"2, ..., a"n), @r = (b"1, b"2, ..., b"n) be two permutations of Z"n = {1, 2, ..., n}. A rise of @p is pair a"i, a"i"+"1 with a"i a"i"+"1. Thus, for i = 1, 2, ..., n - 1, the two pairs a"i, a"i"+"1; b"i, b"i"+"1 are either both rises,
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::027efcfe8f0fe6148fe86858ddadcb8a
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7
Note on Some Convolved Power Sums
Autor: Leonard Carlitz
Publikováno v: SIAM Journal on Mathematical Analysis. 8:701-709
Neuman and Schonbach have obtained explicit formulas for the sum \[S(i,j;N) = \sum\limits_{k = 0}^N {k_i (N - k)^i } \quad (i,j \geqq 0)\] by using known results involving Bernoulli numbers. In the present paper the functions \[\begin{gathered} S(i,j
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::21b5c770379d05eebe3b85fc13aa592e
https://doi.org/10.1137/0508054
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9
Enumeration of matrices of given rank with submatrices of given rank
Autor: John H. Hodges, Leonard Carlitz
Publikováno v: Linear Algebra and its Applications. 16(3):285-291
The authors determine the number of ( n + m )× t matrices A ∗ of rank r + v , over a finite field GF ( q ), whose last m rows are those of a given matrix A of rank r + v over GF ( q ) and whose first n rows have a given rank u .
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d71b15750013500cc168a3558410e395
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10
A test for additive decomposability of irreducibles over a finite field
Autor: Leonard Carlitz, Joel V. Brawley
Publikováno v: Discrete Mathematics. 76(1):61-65
A polynomial h over a field F is said to be additively decomposable over F if there exist polynomials f and g in F [ x ] each of degree >1 such that the roots of h are precisely all sums α + β of roots α of f and β of g . This paper derives a tes
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a4ab287cb3c425bbf0325354ac1921a
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