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Iona College Professor Published in the American Mathematical Monthly

Co-written by Dr. Benjamin Gaines, “The Game of Cycles” is featured in the journal’s December issue

NEW ROCHELLE, N.Y. (December 20, 2021)Dr. Benjamin Gaines, associate professor of mathematics at Iona College, was featured in the December issue of the American Mathematical Monthly— highlighting an article he co-wrote, “The Game of Cycles.”

In the Game of Cycles, players take turns drawing arrows on the edges of a graph. The goal is to be the player to draw an arrow that completes a “cycle” — that is, completely encloses a two-dimensional cell of the graph with arrows all going the same direction around it. However, there's a catch: neither player is allowed to create sinks (where all arrows point inwards at a point) or sources (where all arrows point outwards at a point). This sink-source rule leads to some interesting mathematics, both while playing the game and from a broader topological perspective.

In the article, Gaines describes how to play the Game of Cycles, how to see which player has the winning strategy and observe that the sink-source rule guarantees that if every edge on a (finite, connected) board is marked, there must be a cycle cell somewhere on the board.

The article was also mentioned in a tweet from the Mathematical Association of America, the world’s largest community of mathematicians, students and enthusiasts.

Founded in 1940, Iona College is a master's-granting private, Catholic, coeducational institution of learning in the tradition of the Edmund Rice Christian Brothers. Iona's 45-acre New Rochelle campus and 28-acre Bronxville campus are just 20 miles north of Midtown Manhattan. With a total enrollment of nearly 4,000 students and an alumni base of over 50,000 around the world, Iona is a diverse community of learners and scholars dedicated to academic excellence and the values of justice, peace and service. Iona is highly accredited, offering undergraduate degrees in liberal arts, science, and business administration, as well as Master of Arts, Master of Science and Master of Business Administration degrees and numerous advanced certificate programs. Iona’s LaPenta School of Business is accredited by AACSB International, a prestigious recognition awarded to just five percent of business schools worldwide. The Princeton Review recognized Iona’s on-campus MBA program as a “Best Business School for 2021.” Iona College also recently launched a new, fully online MBA program for even greater flexibility. In July 2021, Iona College and NewYork-Presbyterian announced the establishment of the NewYork-Presbyterian Iona School of Health Sciences, to be principally located on the College’s new campus at 171 White Plains Road, Bronxville, N.Y. Supported by a $20 million gift from NewYork-Presbyterian, the NewYork-Presbyterian Iona School of Health Sciences is expected to offer a new vision for collaborative health care education, modern workforce development, and community care.