Counting Juggling Sequences
{"Image DocumentName": "Counting Juggling Sequences", "Image ImageDescription": "Lemma: The number of all juggling sequences of period \ud835\udc5d, juggled with at most \ud835\udc4f balls, is: \ud835\udc46 \u2264 \ud835\udc4f,\ud835\udc5d = \ud835\udc4f+1 \ud835\udc5d It follows that: Lemma: The number of all \ud835\udc4f-ball juggling sequences of period \ud835\udc5d is: \ud835\udc46 \ud835\udc4f,\ud835\udc5d = \ud835\udc46 \u2264 \ud835\udc4f,\ud835\udc5d \u2013 \ud835\udc46 \u2264 \ud835\udc4f\u22121,\ud835\udc5d = \ud835\udc4f+1 \ud835\udc5d \u2212 \ud835\udc4f \ud835\udc5d However, we have counted each cyclic permutation of every sequence, as well as non-minimal sequences. How can we count the minimal \ud835\udc83-ball juggling sequences of period \ud835\udc91, not counting cyclic permutations of the same sequence as distinct?", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}