BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://colleges.claremont.edu/ccms
X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:America/Los_Angeles
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20230312T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20231105T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20240310T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20241103T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20250309T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20251102T090000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241029T121500
DTEND;TZID=America/Los_Angeles:20241029T131000
DTSTAMP:20260427T061210
CREATED:20240903T234219Z
LAST-MODIFIED:20241023T053311Z
UID:3487-1730204100-1730207400@colleges.claremont.edu
SUMMARY:Sequences with identical autocorrelation spectra (Daniel Katz\, Cal State Northridge)
DESCRIPTION:In this talk\, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.  Resolving the lack of phase information is called the phase problem.  We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.  We investigate the necessary and sufficient conditions for two sequences to be equicorrelational\, where\nwe take into consideration the alphabet from which their terms are drawn.  There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation\, for example\, negating the sequence or writing the sequence in reverse order and then complex conjugating every term.  By an exhaustive search of binary sequences up to length $44$\, we find that nontrivial equicorrelationality among binary sequences does occur\, but is rare.  We say that a positive integer $n$ is {\it unequivocal} to mean that there is no pair of nontrivially equicorrelational binary sequences of length $n$; otherwise $n$ is {\it equivocal}.  For integers $n \leq 44$\, we found that the unequivocal ones are $1$–$8$\, $10$\, $11$\, $13$\, $14$\, $19$\, $22$\, $23$\, $26$\, $29$\, $37$\, and $38$.  We prove that any multiple of a equivocal number is also equivocal\, and pose open questions as to whether there are finitely or infinitely many unequivocal numbers and whether the probability of nontrivial equicorrelationality occurring tends to zero as the sequence length tends to infinity.  (This is joint work with Adeebur Rahman and Michael J Ward.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR