{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECE462Lect8 - Func%on Classica%on Symmetric Func%ons A...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Func%on’Classifca%on’
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Symmetric’Func%ons’ A’func%on’f’is’ totally symmetric ’if’and’only’if’ it’is’unchanged’by’any’permuta%on’of’its’ variables’ f’=’ xy’+’ xz’+’ yz’ f’=’ xy±’+’ x±y’ A’func%on’f’is’ totally symmetric ’if’and’only’if’ it’can’be’speci²ed’by’sta%ng’a’list’of’integers’ A’=’{a 1 ,’a 2 ,…,a m },’0’≤’j’≤’n’so’that’f’=’1’if’and’ only’if’exactly’j’of’the’variables’are’1’ f
Image of page 2
Mixed’Symmetric’Func%ons’ A’func%on’f’is’ mixed symmetric ’if’and’only’if’ it’is’not’totally’symmetric,’but’it’can’be’ changed’into’a’totally’symmetric’func%on’by’ replacing’some’of’its’variables’by’their’ complements’ f’=’ xy±z±’ Replace’y±’by’y’and’z±’by’z’
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Symmetric’Func%ons’ A’func%on’f’is’ symmetric ’if’it’is’either’totally’ or’mixed’symmetric’
Image of page 4
Posi%ve’and’Nega%ve’Func%ons’ A’func%on’f(x 1 ,’x 2 ,…,x n )’is’ posi0ve ’in’x i ’if’and’ only’if’it’is’possible’to’write’a’sum-of-products’ expression’for’f’in’which’x i
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern