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1

A generalization of Descartes’ rule of signs and fundamental theorem of algebra

Pentti Haukkanen, Timo Tossavainen

Journal:

Applied Mathematics and Computation

Year:

2011

Language:

english

File:

PDF, 171 KB

english, 2011

2

On generalized Fibonacci and Lucas polynomials

Ayse Nalli, Pentti Haukkanen

Journal:

Chaos, Solitons & Fractals

Year:

2009

Language:

english

File:

PDF, 181 KB

english, 2009

3

An abstract Möbius inversion formula with number-theoretic applications

Pentti Haukkanen

Journal:

Discrete Mathematics

Year:

1995

Language:

english

File:

PDF, 552 KB

english, 1995

4

On a gcd-sum function

Pentti Haukkanen

Journal:

Aequationes Mathematicae

Year:

2008

Language:

english

File:

PDF, 159 KB

english, 2008

5

An analogue of Ramanujan’s sum with respect to regular integers (modr)

Pentti Haukkanen, László Tóth

Journal:

The Ramanujan Journal

Year:

2012

Language:

english

File:

PDF, 569 KB

english, 2012

6

A topological approach to divisibility of arithmetical functions and GCD matrices

Haukkanen, Pentti

Journal:

Linear and Multilinear Algebra

Year:

2012

Language:

english

File:

PDF, 135 KB

english, 2012

7

On a convolution of linear recurring sequences over finite fields

Pentti Haukkanen

Journal:

Journal of Algebra

Year:

1992

Language:

english

File:

PDF, 179 KB

english, 1992

8

Menon’s identity with respect to a generalized divisibility relation

Pentti Haukkanen

Journal:

Aequationes Mathematicae

Year:

2005

Language:

english

File:

PDF, 126 KB

english, 2005

9

Smith meets Smith: Smith normal form of Smith matrix

Ilmonen, Pauliina, Haukkanen, Pentti

Journal:

Linear and Multilinear Algebra

Year:

2011

Language:

english

File:

PDF, 120 KB

english, 2011

10

ASYMPTOTICS FOR NUMBERS OF LINE SEGMENTS AND LINES IN A SQUARE GRID

HAUKKANEN, PENTTI, MERIKOSKI, JORMA K.

Journal:

International Journal of Number Theory

Year:

2012

Language:

english

File:

PDF, 127 KB

english, 2012

11

On Direct and Inverse Proportionality

Markku Halmetoja, Pentti Haukkanen, Teuvo Laurinolli, Jorma K. Merikoski, Timo Tossavainen and Ari Virtanen

Journal:

American Mathematical Monthly

Year:

2007

Language:

english

File:

PDF, 760 KB

english, 2007

12

On Smith's determinant

Pentti Haukkanen, Jun Wang, Juha Sillanpää

Journal:

Linear Algebra and its Applications

Year:

1997

Language:

english

File:

PDF, 650 KB

english, 1997

13

Arithmetical identities of the Brauer-Rademacher type

Pentti Haukkanen, P. J. McCarthy

Journal:

Aequationes Mathematicae

Year:

1990

Language:

english

File:

PDF, 778 KB

english, 1990

14

A generalization of the Subbarao identity

Pentti Haukkanen

Journal:

Aequationes Mathematicae

Year:

1988

Language:

english

File:

PDF, 152 KB

english, 1988

15

Formulas for the number of gridlines

Anne-Maria Ernvall-Hytönen, Kaisa Matomäki, Pentti Haukkanen, Jorma K. Merikoski

Journal:

Monatshefte für Mathematik

Year:

2011

Language:

english

File:

PDF, 185 KB

english, 2011

16

Different aspects of the monotonicity of a function

Tossavainen, Timo, Haukkanen, Pentti, Pesonen, Martti

Journal:

International Journal of Mathematical Education

Year:

2013

Language:

english

File:

PDF, 349 KB

english, 2013

17

A UNIQUE FACTORIZATION IN COMMUTATIVE MÖBIUS MONOIDS

SCHWAB, EMIL DANIEL, HAUKKANEN, PENTTI

Journal:

International Journal of Number Theory

Year:

2008

Language:

english

File:

PDF, 192 KB

english, 2008

18

Arithmetic functions in an algebraic setting

Haukkanen, Pentti, Sivaramakrishnan, R.

Journal:

Tsukuba Journal of Mathematics

Year:

1991

Language:

english

File:

PDF, 615 KB

english, 1991

19

Bounds for sine and cosine via eigenvalue estimation

Haukkanen, Pentti, Mattila, Mika, Merikoski, Jorma K., Kovacec, Alexander

Journal:

Special Matrices

Year:

2014

Language:

english

File:

PDF, 397 KB

english, 2014

20

On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

Merikoski, Jorma K., Haukkanen, Pentti, Mattila, Mika, Tossavainen, Timo

Journal:

Special Matrices

Language:

english

File:

PDF, 439 KB

english

21

Higher-dimensional gcd matrices

Pentti Haukkanen

Journal:

Linear Algebra and its Applications

Year:

1992

Language:

english

File:

PDF, 468 KB

english, 1992

22

On meet matrices on posets

Pentti Haukkanen

Journal:

Linear Algebra and its Applications

Year:

1996

Language:

english

File:

PDF, 680 KB

english, 1996

23

On eigenvalues of meet and join matrices associated with incidence functions

Pauliina Ilmonen, Pentti Haukkanen, Jorma K. Merikoski

Journal:

Linear Algebra and its Applications

Year:

2008

Language:

english

File:

PDF, 166 KB

english, 2008

24

On the divisibility of meet and join matrices

Ismo Korkee, Pentti Haukkanen

Journal:

Linear Algebra and its Applications

Year:

2008

Language:

english

File:

PDF, 226 KB

english, 2008

25

On a generalized convolution of incidence functions

Pentti Haukkanen

Journal:

Discrete Mathematics

Year:

2000

Language:

english

File:

PDF, 91 KB

english, 2000

26

Bounds for determinants of meet matrices associated with incidence functions

Ismo Korkee, Pentti Haukkanen

Journal:

Linear Algebra and its Applications

Year:

2001

Language:

english

File:

PDF, 100 KB

english, 2001

27

On meet and join matrices associated with incidence functions

Ismo Korkee, Pentti Haukkanen

Journal:

Linear Algebra and its Applications

Year:

2003

Language:

english

File:

PDF, 208 KB

english, 2003

28

On a general form of join matrices associated with incidence functions

Ismo Korkee, Pentti Haukkanen

Journal:

Aequationes Mathematicae

Year:

2008

Language:

english

File:

PDF, 766 KB

english, 2008

29

Meet and join matrices in the poset of exponential divisors

Ismo Korkee, Pentti Haukkanen

Journal:

Proceedings Mathematical Sciences

Year:

2009

Language:

english

File:

PDF, 179 KB

english, 2009

30

Some properties of row-adjusted meet and join matrices

Mattila, Mika, Haukkanen, Pentti

Journal:

Linear and Multilinear Algebra

Year:

2012

Language:

english

File:

PDF, 161 KB

english, 2012

31

Asymptotics of the number of threshold functions on a two-dimensional rectangular grid

Pentti Haukkanen, Jorma K. Merikoski

Journal:

Discrete Applied Mathematics

Year:

2013

Language:

english

File:

PDF, 191 KB

english, 2013

32

On the positive definiteness and eigenvalues of meet and join matrices

Mattila, Mika, Haukkanen, Pentti

Journal:

Discrete Mathematics

Year:

2014

Language:

english

File:

PDF, 456 KB

english, 2014

33

Determinant and inverse of join matrices on two sets

Mattila, Mika, Haukkanen, Pentti

Journal:

Linear Algebra and its Applications

Year:

2013

Language:

english

File:

PDF, 303 KB

english, 2013

34

On unitary analogs of GCD reciprocal LCM matrices

Haukkanen, Pentti, Ilmonen, Pauliina, Nalli, Ayse, Sillanpää, Juha

Journal:

Linear and Multilinear Algebra

Year:

2010

Language:

english

File:

PDF, 385 KB

english, 2010

35

Some analogues of smith's determinant

Haukkanen, Pentti, Sillanpää, Juha

Journal:

Linear and Multilinear Algebra

Year:

1996

Language:

english

File:

PDF, 437 KB

english, 1996

36

Perpendicularity in an Abelian Group

Haukkanen, Pentti, Mattila, Mika, Merikoski, Jorma K., Tossavainen, Timo

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2013

Language:

english

File:

PDF, 163 KB

english, 2013

37

Studying the singularity of LCM-type matrices via semilattice structures and their Möbius functions

Haukkanen, Pentti, Mattila, Mika, Mäntysalo, Jori

Journal:

Journal of Combinatorial Theory, Series A

Year:

2015

Language:

english

File:

PDF, 518 KB

english, 2015

38

On a general form of meet matrices associated with incidence functions

Korkee, Ismo, Haukkanen, Pentti

Journal:

Linear and Multilinear Algebra

Year:

2005

Language:

english

File:

PDF, 149 KB

english, 2005

39

An upper bound for the ℒP norm of a GCD-related matrix

Haukkanen, Pentti

Journal:

Journal of Inequalities and Applications

Year:

2006

Language:

english

File:

PDF, 172 KB

english, 2006

40

An arithmetical equation with respect to regular convolutions

Haukkanen, Pentti

Journal:

Aequationes Mathematicae

Year:

2017

Language:

english

File:

PDF, 461 KB

english, 2017

41

Derivation of arithmetical functions under the Dirichlet convolution

Haukkanen, Pentti

Journal:

International Journal of Number Theory

Year:

2017

Language:

english

File:

PDF, 126 KB

english, 2017

42

Determinant and Inverse of Meet and Join Matrices

Altinisik, Ercan, Tuglu, Naim, Haukkanen, Pentti

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2007

Language:

english

File:

PDF, 1.86 MB

english, 2007

43

Notes on the divisibility of GCD and LCM Matrices

Haukkanen, Pentti, Korkee, Ismo

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2005

Language:

english

File:

PDF, 1.85 MB

english, 2005

44

Some characterizations of specially multiplicative functions

Haukkanen, Pentti

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

2003

Language:

english

File:

PDF, 1.81 MB

english, 2003

45

Some characterizations of totients

Haukkanen, Pentti

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

1996

Language:

english

File:

PDF, 2.40 MB

english, 1996

46

An identity for a class of arithmetical functions of several variables

Haukkanen, Pentti

Journal:

International Journal of Mathematics and Mathematical Sciences

Year:

1993

Language:

english

File:

PDF, 1.92 MB

english, 1993

47

A lattice-theoretic approach to the Bourque–Ligh conjecture

Korkee, Ismo, Mattila, Mika, Haukkanen, Pentti

Journal:

Linear and Multilinear Algebra

Year:

2018

Language:

english

File:

PDF, 2.28 MB

english, 2018

48

Inertia, positive definiteness and ℓ norm of GCD and LCM matrices and their unitary analogs

Haukkanen, Pentti, Tóth, László

Journal:

Linear Algebra and its Applications

Year:

2018

Language:

english

File:

PDF, 429 KB

english, 2018

49

On the Kesava Menon norm of semimultiplicative functions

Haukkanen, Pentti

Journal:

Aequationes Mathematicae

Year:

2019

Language:

english

File:

PDF, 284 KB

english, 2019

50

Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture

Haukkanen, Pentti, Mattila, Mika, Mäntysalo, Jori

Journal:

Journal of Combinatorial Theory, Series A

Year:

2020

File:

PDF, 482 KB

2020