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Beyoncé Knowles and Jay-Z are believed to have called new daughter Blue because of the rapper's string of successful albums of a similar name.
Jay-Z's chart-topping records The Blueprint, The Blueprint 2: The Gift & The Curse and The Blueprint 3, could be behind the unusual choice for a little girl.
Ivy is thought to be in reference to the couple's love of the number 4, which is IV in Roman numerals.
'We all have special numbers in our lives, and 4 is that for me,' Beyoncé, 30, told Billboard last year.
'It's the day I was born. My mother's birthday, and a lot of my friends' birthdays, are on the 4th; 4 April is my wedding date.'
News of Blue Ivy's birth at Lennox Hill Hospital, New York, at the weekend, sparked a long-list of Twitter well-wishes from fellow celebrities and friends of Jay-Z, 42, and Bey.
'Welcome to the world Blue! We love you already,' Tweeted actress Gwyneth Paltrow, 39.
And Rihanna, 23, wrote: 'Welcome to the world princess Carter! Love Aunty Rih.'
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Esme Riley