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DTSTART;TZID=America/Toronto:20251113T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-pierre
SUMMARY:Algebraic and enumerative combinatorics seminar-Pierre Popoli
CLASS:PUBLIC
DESCRIPTION:TITLE: Generalized Abelian Complexities for Pisot-Type Substitu
 tive\nSequences\n\nSpeaker\n Pierre Popoli\n\nAffiliation\n University of 
 Wtaerloo\n\nLocation\n MC 6029\n\nABSTRACT: Two finite words are said to 
 be abelian equivalent if one\nis a permutation of the letters of the othe
 r. For an infinite word\,\none can investigate the associated complexity 
 function\, called\nAbelian complexity\, which is a classical object of st
 udy in\ncombinatorics on words. In particular\, many works study the abel
 ian\ncomplexity of automatic sequences\, where a longstanding conjecture\
 nstates that the abelian complexity of an automatic sequence is a\nregula
 r sequence. We have studied when the abelian complexity can be\ncomputed 
 efficiently\, in particular using the theorem prover Walnut.\nTo this end
 \, we study words that are fixed points of Pisot-type\nsubstitution and p
 rove that these words satisfy the conjecture. If\ntime permits\, I will 
 present k-abelian complexities\, which\nare intermediate complexities bet
 ween the abelian complexity and the\nfactor complexity. I will also expla
 in how our results can be\nextended to these\ncomplexities and how we can 
 obtain a two-dimensional\nlinear representation of some examples. This t
 alk is based on joint\nwork with J-M Couvreur\, M. Delacourt\, N. Ollinge
 r\, J. Shallit\, and M.\nStipulanti (arXiv: 2504.13584).\n\nTHERE WILL BE 
 A PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT THE\nBEGINNING GRADUATE LE
 VEL STARTING AT 1:30PM.
DTSTAMP:20260406T150202Z
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