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UID:20250809T164919EDT-18597PAxHH@132.216.98.100
DTSTAMP:20250809T204919Z
DESCRIPTION:Enumeration of binomial coefficients by their p-adic valuations
 \n\nIn 1947 Nathan Fine obtained a beautiful formula for the number of bin
 omial coefficients binomial(n\, m)\, for fixed n\, that are not divisible 
 by p: Write n in base p\, add 1 to each digit\, and multiply them all toge
 ther. Subsequently\, many authors found formulas counting binomial coeffic
 ients with p-adic valuation alpha for particular values of p and alpha\, b
 ut a general formula remained elusive. We give a matrix product\, generali
 zing Fine's result\, for the generating function counting binomial coeffic
 ients by their p-adic valuations. A further generalization counts multinom
 ial coefficients by their p-adic valuations.\n
DTSTART:20180420T173000Z
DTEND:20180420T183000Z
LOCATION:Room PK-4323\, CA\, H2X 2Y7\, Pav. André-Aisenstadt\, 201 Ave. Pre
 sident-Kennedy
SUMMARY:Eric Rowland\, Hofstra University
URL:/mathstat/channels/event/eric-rowland-hofstra-univ
 ersity-286620
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