Singmaster
Singmaster is a surname. Notable people with the surname include: * C. F. and Mary Singmaster, owners of the C.F. and Mary Singmaster House * David Singmaster (1938–2023), British mathematician, after whom Singmaster's conjecture is named * Elsie Singmaster (1879–1958), American writer See also * Songmaster ''Songmaster'' (1980) is a science fiction novel by American writer Orson Scott Card. The story of the ''Songmaster'' occurs in a future human empire, and follows Ansset, a beautiful young boy whose perfect singing voice has the power of amplif ...

David Singmaster
David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is most famous for being an early adopter and enthusiastic promoter of the Rubik's Cube. His ''Notes on Rubik's "Magic Cube"'' which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing one of the first published solutions. The book contained his cube notation which allowed the recording of Rubik's Cube moves, and which quickly became the standard. He is both a puzzle historian and a composer of puzzles, and many of his puzzles have been published in newspapers and magazines. In combinatorial number theory, Singmaster's conjecture states that there is an upper bound on the number of times a number other than 1 can appear in Pascal's triangle. Career David Singmaster was a student at the Californi ...
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Elsie Singmaster
Elsie Singmaster Lewars (August 29, 1879 – September 30, 1958) was an American author from Macungie, Pennsylvania, who has been described as "perhaps Macungie's most famous citizen". She was a Newbery Honor recipient in 1934. Early life and education Singmaster was born on August 29, 1879, in Schuylkill Haven, Pennsylvania, to parents of German ancestry. She was educated at Allentown High School and West Chester Normal School, before studying at Cornell University from 1898 to 1900. She then attended Radcliffe College, where she graduated in 1907. In 1912, she married musician and English professor Harold Steck Lewars. She added his surname to hers but continued to publish as Elsie Singmaster. She was pregnant with Lewars' child when he died at the age of 33 in March 1915. Their baby, Singmaster's only child, died two months later in May. Career Singmaster wrote many short stories and books between 1905 and 1950. Her first published short story was ''The Lèse-Majesté of Ha ...
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Singmaster's Conjecture
Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). It is clear that the only number that appears infinitely many times in Pascal's triangle is 1, because any other number ''x'' can appear only within the first ''x'' + 1 rows of the triangle. Statement Let ''N''(''a'') be the number of times the number ''a'' > 1 appears in Pascal's triangle. In big O notation, the conjecture is: :N(a) = O(1). Known bound Singmaster (1971) showed that :N(a) = O(\log a). Abbot, Erdős, and Hanson (1974) (see References) refined the estimate to: :N(a) = O\left(\frac\right). The best currently known (unconditional) bound is :N(a) = O\left(\frac\right), and is due to Kane (2007). Abbot, Erdős, and Hanson note that condit ...
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