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ICE-TCS seminar: Pascal's matrix and incidence algebras

  • 9.4.2015, 14:00 - 15:00
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Date and time: Thursday, 9 April 2015, at 2pm
Place: Room M102
Title: Pascal's matrix and incidence algebras
Speaker: Anders Claesson (University of Strathclyde, UK; http://akc.is/)

Abstract:
The Pascal matrix, P, is an upper diagonal matrix whose entries are the
binomial coefficients. In 1993 Call and Velleman demonstrated that it
satisfies the intriguing relation P = exp(H) in which H has the numbers
1, 2, 3, etc. on its superdiagonal and zeros elsewhere. We generalize
this identity to the incidence algebras I(A^*) and I(S) of functions on
words and permutations, respectively.  In I(A^*) the entries of P and H
count subwords; in I(S) they count occurrences of permutation patterns.



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