Lambek–Moser theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Lambek–Moser theorem" in English language version.

refsWebsite

Global rank English rank

11doi.org

2^nd place

8ams.org

451^st place

277^th place

6jstor.org

26^th place

20^th place

3utexas.edu

916^th place

706^th place

3books.google.com

3^rd place

2ust.hk

low place

2zbmath.org

1,923^rd place

1,068^th place

1projecteuclid.org

3,707^th place

2,409^th place

1semanticscholar.org

11^th place

8^th place

1emis.de

low place

1arxiv.org

69^th place

59^th place

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Wild 1955. Wild, Roy E. (1955), "On the number of primitive Pythagorean triangles with area less than $n$ ", Pacific Journal of Mathematics, 5: 85–91, doi:10.2140/pjm.1955.5.85, MR 0067912
Lambek & Moser 1954; Honsberger 1970, pp. 95–96; Fraenkel 1977. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Fraenkel, Aviezri S. (1977), "Complementary systems of integers", The American Mathematical Monthly, 84 (2): 114–115, doi:10.2307/2319931, JSTOR 2319931, MR 0429815
Angel 1964. Angel, Myer (1964), "Partitions of the natural numbers", Canadian Mathematical Bulletin, 7 (2): 219–236, doi:10.4153/CMB-1964-020-1, MR 0161826, S2CID 123729929
Lambek & Moser 1954; Roberts 1992. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Brun 1931; Lehmer 1932. Brun, Viggo (1931), "Rechenregel zur Bildung der $n$ -ten Primzahl" [Calculating rules to build the $n$ th prime], Norsk Matematisk Tidsskrift (in Norwegian), 13: 73–79, Zbl 0003.14902, as cited by Lambek & Moser 1954 Lehmer, D. H. (1932), "An inversive algorithm", Bulletin of the American Mathematical Society, 38 (10): 693–694, doi:10.1090/S0002-9904-1932-05496-9, MR 1562488
Honsberger 1970, pp. 97–100; Dos Reis & Silberger 1990; Roberts 1992. Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Lambek 1994. Lambek, Joachim (1994), "Some Galois connections in elementary number theory", Journal of Number Theory, 47 (3): 371–377, doi:10.1006/jnth.1994.1043, MR 1278405
Rayleigh 1894; Beatty 1926; Honsberger 1970, pp. 93–95; Chamberland 2017. John William Strutt, Baron Rayleigh (1894), The Theory of Sound, vol. 1 (2nd ed.), Macmillan, p. 123 Beatty, Samuel (1926), "Problem 3173", The American Mathematical Monthly, 33 (3): 159, doi:10.2307/2300153, JSTOR 2300153; Solutions by Beatty, A. Ostrowski, J. Hyslop, and A. C. Aitken, vol. 34 (1927), pp. 159–160, JSTOR 2298716 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Chamberland, Marc (2017), "Beatty sequences", Single Digits: In Praise of Small Numbers, Princeton University Press, pp. 32–33, ISBN 978-0-691-17569-0

arxiv.org (Global: 69^th place; English: 59^th place)

Ginosar 2014. Ginosar, Yuval (2014), "On the Lambek–Moser theorem", Integers, 14: A09:1–A09:4, arXiv:1207.5633

books.google.com (Global: 3^rd place; English: 3^rd place)

Lambek & Moser 1954; Roberts 1992. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Honsberger 1970, pp. 97–100; Dos Reis & Silberger 1990; Roberts 1992. Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Rayleigh 1894; Beatty 1926; Honsberger 1970, pp. 93–95; Chamberland 2017. John William Strutt, Baron Rayleigh (1894), The Theory of Sound, vol. 1 (2nd ed.), Macmillan, p. 123 Beatty, Samuel (1926), "Problem 3173", The American Mathematical Monthly, 33 (3): 159, doi:10.2307/2300153, JSTOR 2300153; Solutions by Beatty, A. Ostrowski, J. Hyslop, and A. C. Aitken, vol. 34 (1927), pp. 159–160, JSTOR 2298716 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Chamberland, Marc (2017), "Beatty sequences", Single Digits: In Praise of Small Numbers, Princeton University Press, pp. 32–33, ISBN 978-0-691-17569-0

doi.org (Global: 2^nd place; English: 2^nd place)

Lambek & Moser 1954. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078
Wild 1955. Wild, Roy E. (1955), "On the number of primitive Pythagorean triangles with area less than $n$ ", Pacific Journal of Mathematics, 5: 85–91, doi:10.2140/pjm.1955.5.85, MR 0067912
Boas 1985. Boas, Ralph P. (January 1985), "Inverse functions", The College Mathematics Journal, 16 (1): 42–47, doi:10.1080/07468342.1985.11972848, JSTOR 2686627
Lambek & Moser 1954; Honsberger 1970, pp. 95–96; Fraenkel 1977. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Fraenkel, Aviezri S. (1977), "Complementary systems of integers", The American Mathematical Monthly, 84 (2): 114–115, doi:10.2307/2319931, JSTOR 2319931, MR 0429815
Angel 1964. Angel, Myer (1964), "Partitions of the natural numbers", Canadian Mathematical Bulletin, 7 (2): 219–236, doi:10.4153/CMB-1964-020-1, MR 0161826, S2CID 123729929
Lambek & Moser 1954; Roberts 1992. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Brun 1931; Lehmer 1932. Brun, Viggo (1931), "Rechenregel zur Bildung der $n$ -ten Primzahl" [Calculating rules to build the $n$ th prime], Norsk Matematisk Tidsskrift (in Norwegian), 13: 73–79, Zbl 0003.14902, as cited by Lambek & Moser 1954 Lehmer, D. H. (1932), "An inversive algorithm", Bulletin of the American Mathematical Society, 38 (10): 693–694, doi:10.1090/S0002-9904-1932-05496-9, MR 1562488
Honsberger 1970, pp. 97–100; Dos Reis & Silberger 1990; Roberts 1992. Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Dijkstra 1982. Dijkstra, Edsger W. (1982), "Lambek and Moser revisited", in Broy, Manfred; Schmidt, Gunther (eds.), Theoretical Foundations of Programming Methodology: Lecture Notes of an International Summer School, directed by F. L. Bauer, E. W. Dijkstra and C. A. R. Hoare, NATO Advanced Study Institutes Series, Series C – Mathematical and Physical Sciences, vol. 91, D. Reidel Publishing Co., pp. 19–23, doi:10.1007/978-94-009-7893-5_2, ISBN 978-90-277-1462-6, Zbl 0533.40001
Lambek 1994. Lambek, Joachim (1994), "Some Galois connections in elementary number theory", Journal of Number Theory, 47 (3): 371–377, doi:10.1006/jnth.1994.1043, MR 1278405
Rayleigh 1894; Beatty 1926; Honsberger 1970, pp. 93–95; Chamberland 2017. John William Strutt, Baron Rayleigh (1894), The Theory of Sound, vol. 1 (2nd ed.), Macmillan, p. 123 Beatty, Samuel (1926), "Problem 3173", The American Mathematical Monthly, 33 (3): 159, doi:10.2307/2300153, JSTOR 2300153; Solutions by Beatty, A. Ostrowski, J. Hyslop, and A. C. Aitken, vol. 34 (1927), pp. 159–160, JSTOR 2298716 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Chamberland, Marc (2017), "Beatty sequences", Single Digits: In Praise of Small Numbers, Princeton University Press, pp. 32–33, ISBN 978-0-691-17569-0

emis.de (Global: low place; English: low place)

Ginosar 2014. Ginosar, Yuval (2014), "On the Lambek–Moser theorem", Integers, 14: A09:1–A09:4, arXiv:1207.5633

jstor.org (Global: 26^th place; English: 20^th place)

Lambek & Moser 1954. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078
Boas 1985. Boas, Ralph P. (January 1985), "Inverse functions", The College Mathematics Journal, 16 (1): 42–47, doi:10.1080/07468342.1985.11972848, JSTOR 2686627
Lambek & Moser 1954; Honsberger 1970, pp. 95–96; Fraenkel 1977. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Fraenkel, Aviezri S. (1977), "Complementary systems of integers", The American Mathematical Monthly, 84 (2): 114–115, doi:10.2307/2319931, JSTOR 2319931, MR 0429815
Lambek & Moser 1954; Roberts 1992. Lambek, Joachim; Moser, Leo (August–September 1954), "Inverse and complementary sequences of natural numbers", The American Mathematical Monthly, 61 (7): 454–458, doi:10.1080/00029890.1954.11988496, JSTOR 2308078 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Honsberger 1970, pp. 97–100; Dos Reis & Silberger 1990; Roberts 1992. Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Roberts, Joe (1992), Lure of the Integers, MAA Spectrum, Washington, DC: Mathematical Association of America, p. 11, doi:10.2307/40148160, ISBN 0-88385-502-X, JSTOR 40148160, MR 1189138
Rayleigh 1894; Beatty 1926; Honsberger 1970, pp. 93–95; Chamberland 2017. John William Strutt, Baron Rayleigh (1894), The Theory of Sound, vol. 1 (2nd ed.), Macmillan, p. 123 Beatty, Samuel (1926), "Problem 3173", The American Mathematical Monthly, 33 (3): 159, doi:10.2307/2300153, JSTOR 2300153; Solutions by Beatty, A. Ostrowski, J. Hyslop, and A. C. Aitken, vol. 34 (1927), pp. 159–160, JSTOR 2298716 Honsberger, Ross (1970), "Essay 12: Complementary sequences", Ingenuity in Mathematics, New Mathematical Library, vol. 23, New York: Random House, Inc., pp. 93–110, ISBN 0-394-70923-3, MR 3155264 Chamberland, Marc (2017), "Beatty sequences", Single Digits: In Praise of Small Numbers, Princeton University Press, pp. 32–33, ISBN 978-0-691-17569-0

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

Wild 1955. Wild, Roy E. (1955), "On the number of primitive Pythagorean triangles with area less than $n$ ", Pacific Journal of Mathematics, 5: 85–91, doi:10.2140/pjm.1955.5.85, MR 0067912

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Angel 1964. Angel, Myer (1964), "Partitions of the natural numbers", Canadian Mathematical Bulletin, 7 (2): 219–236, doi:10.4153/CMB-1964-020-1, MR 0161826, S2CID 123729929

ust.hk (Global: low place; English: low place)

math.ust.hk

There appears to be no consistent name for these curves in the literature on the Lambek–Moser theorem. Both Dijkstra (1980) and Garry (1997) draw these curves and note their reflection property but do not distinguish the curves from the functions they graph nor give them a separate name. A histogram is a type of bar chart for a discrete sequence of data values; the curves called histograms here resemble the histograms of the sequence of function values in this sense. Dijkstra, Edsger W. (1980), On a theorem by Lambek and Moser (PDF), Report EWD753, University of Texas Garry, Y. K. K. (1997), "Inverse sequences and complementary sequences" (PDF), Mathematical Excalibur, 3 (4): 2
Garry 1997. Garry, Y. K. K. (1997), "Inverse sequences and complementary sequences" (PDF), Mathematical Excalibur, 3 (4): 2

utexas.edu (Global: 916^th place; English: 706^th place)

cs.utexas.edu

There appears to be no consistent name for these curves in the literature on the Lambek–Moser theorem. Both Dijkstra (1980) and Garry (1997) draw these curves and note their reflection property but do not distinguish the curves from the functions they graph nor give them a separate name. A histogram is a type of bar chart for a discrete sequence of data values; the curves called histograms here resemble the histograms of the sequence of function values in this sense. Dijkstra, Edsger W. (1980), On a theorem by Lambek and Moser (PDF), Report EWD753, University of Texas Garry, Y. K. K. (1997), "Inverse sequences and complementary sequences" (PDF), Mathematical Excalibur, 3 (4): 2
Dijkstra 1980. Dijkstra, Edsger W. (1980), On a theorem by Lambek and Moser (PDF), Report EWD753, University of Texas
Dijkstra 1982. Dijkstra, Edsger W. (1982), "Lambek and Moser revisited", in Broy, Manfred; Schmidt, Gunther (eds.), Theoretical Foundations of Programming Methodology: Lecture Notes of an International Summer School, directed by F. L. Bauer, E. W. Dijkstra and C. A. R. Hoare, NATO Advanced Study Institutes Series, Series C – Mathematical and Physical Sciences, vol. 91, D. Reidel Publishing Co., pp. 19–23, doi:10.1007/978-94-009-7893-5_2, ISBN 978-90-277-1462-6, Zbl 0533.40001

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Brun 1931; Lehmer 1932. Brun, Viggo (1931), "Rechenregel zur Bildung der $n$ -ten Primzahl" [Calculating rules to build the $n$ th prime], Norsk Matematisk Tidsskrift (in Norwegian), 13: 73–79, Zbl 0003.14902, as cited by Lambek & Moser 1954 Lehmer, D. H. (1932), "An inversive algorithm", Bulletin of the American Mathematical Society, 38 (10): 693–694, doi:10.1090/S0002-9904-1932-05496-9, MR 1562488
Dijkstra 1982. Dijkstra, Edsger W. (1982), "Lambek and Moser revisited", in Broy, Manfred; Schmidt, Gunther (eds.), Theoretical Foundations of Programming Methodology: Lecture Notes of an International Summer School, directed by F. L. Bauer, E. W. Dijkstra and C. A. R. Hoare, NATO Advanced Study Institutes Series, Series C – Mathematical and Physical Sciences, vol. 91, D. Reidel Publishing Co., pp. 19–23, doi:10.1007/978-94-009-7893-5_2, ISBN 978-90-277-1462-6, Zbl 0533.40001

Lambek–Moser theorem (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

arxiv.org (Global: 69th place; English: 59th place)

books.google.com (Global: 3rd place; English: 3rd place)

doi.org (Global: 2nd place; English: 2nd place)